-y^2=8y-195

Solution for -y^2=8y-195 equation:

-y^2=8y-195

We move all terms to the left:

-y^2-(8y-195)=0

We add all the numbers together, and all the variables

-1y^2-(8y-195)=0

We get rid of parentheses

-1y^2-8y+195=0

a = -1; b = -8; c = +195;
Δ = b2-4ac
Δ = -82-4·(-1)·195
Δ = 844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{211}}{2*-1}=\frac{8-2\sqrt{211}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{211}}{2*-1}=\frac{8+2\sqrt{211}}{-2}
$