What are the solutions to the equation ((5x-4)*(5x+4))/4 =((3x-1)^2-9)/2 ?

The solutions to the equation ((5x-4)*(5x+4))/4 =((3x-1)^2-9)/2 are x=-12/7 ,x=0

Find the zeros of ((5x-4)*(5x+4))/4 =((3x-1)^2-9)/2

The zeros of ((5x-4)*(5x+4))/4 =((3x-1)^2-9)/2 are x=-12/7 ,x=0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{( 5 x - 4 ) \cdot ( 5 x + 4 )}{4} = \frac{( 3 x - 1 ) ^{2} - 9}{2}

x = - \frac{12}{7}, x = 0

Decimal Notation

x = - 1.71428 \dots, x = 0

Solution steps

\frac{( 5 x - 4 ) ( 5 x + 4 )}{4} = \frac{( 3 x - 1 ) ^{2} - 9}{2}

Find Least Common Multiplier of

4, 2 : 4

Multiply by LCM=

4

\frac{( 5 x - 4 ) ( 5 x + 4 )}{4} \cdot 4 = \frac{( 3 x - 1 ) ^{2} - 9}{2} \cdot 4

Simplify

(5 x - 4) (5 x + 4) = 2 ((3 x - 1)^{2} - 9)

Expand

(5 x - 4) (5 x + 4) : 25 x^{2} - 16

Expand

2 ((3 x - 1)^{2} - 9) : 18 x^{2} - 12 x - 16

25 x^{2} - 16 = 18 x^{2} - 12 x - 16

Switch sides

18 x^{2} - 12 x - 16 = 25 x^{2} - 16

Move

16

to the left side

18 x^{2} - 12 x = 25 x^{2}

Move

25 x^{2}

to the left side

- 7 x^{2} - 12 x = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 ( - 7 ) \cdot 0}{2 ( - 7 )}

(- 12)^{2} - 4 (- 7) \cdot 0 = 12

x_{1, 2} = \frac{- ( - 12 ) \pm 12}{2 ( - 7 )}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 12}{2 ( - 7 )}, x_{2} = \frac{- ( - 12 ) - 12}{2 ( - 7 )}

x = \frac{- ( - 12 ) + 12}{2 ( - 7 )} : - \frac{12}{7}

x = \frac{- ( - 12 ) - 12}{2 ( - 7 )} : 0

The solutions to the quadratic equation are:

x = - \frac{12}{7}, x = 0

12 y^{2} + 23 y + 5 = 0

- \frac{3}{2} x^{- \frac{3}{2}}

12 m^{3} - 14 m^{2} - 30 m + 35

9 (t + 2) = 3 (3 t - 2)

\frac{1}{5} t^{2} - 36 = 0

What are the solutions to the equation ((5x-4)*(5x+4))/4 =((3x-1)^2-9)/2 ?
The solutions to the equation ((5x-4)*(5x+4))/4 =((3x-1)^2-9)/2 are x=-12/7 ,x=0
Find the zeros of ((5x-4)*(5x+4))/4 =((3x-1)^2-9)/2
The zeros of ((5x-4)*(5x+4))/4 =((3x-1)^2-9)/2 are x=-12/7 ,x=0