What is ((t^2+t))/2 sqrt(5)=s ?

The solution to ((t^2+t))/2 sqrt(5)=s is Parabola with (h,k)=(-(sqrt(5))/2 ,-5/8),p= 1/2

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((t^2+t))/2 sqrt(5)=s

\frac{( t ^{2} + t )}{2} 5 = s

(h, k) = (- \frac{5}{2}, - \frac{5}{8}), p = \frac{1}{2}

Solution steps

\frac{t ^{2} + t}{2} 5 = s

Rewrite

\frac{t ^{2} + t}{2} 5 = s

in the standard form

4 \cdot \frac{1}{2} (s - (- \frac{5}{8})) = (t - (- \frac{5}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{5}{2}, - \frac{5}{8}), p = \frac{1}{2}

- \frac{8 y + 1}{2 x ^{2}} = - \frac{4 y}{x ^{2}} - \frac{1}{y}

yy = \frac{8 x}{3} + {2}

y - 7 x^{2} = 2

4^{2} + 4 y^{2} - 20 x + 40 y = - 5

- x^{2} + 16 x + 32 y = 128

What is ((t^2+t))/2 sqrt(5)=s ?
The solution to ((t^2+t))/2 sqrt(5)=s is Parabola with (h,k)=(-(sqrt(5))/2 ,-5/8),p= 1/2