96+y(-y)=20

Solution for 96+y(-y)=20 equation:

96+y(-y)=20

We move all terms to the left:

96+y(-y)-(20)=0

We add all the numbers together, and all the variables

y(-1y)+96-20=0

We add all the numbers together, and all the variables

y(-1y)+76=0

We multiply parentheses

-1y^2+76=0

a = -1; b = 0; c = +76;
Δ = b2-4ac
Δ = 02-4·(-1)·76
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{19}}{2*-1}=\frac{0-4\sqrt{19}}{-2}
=-\frac{4\sqrt{19}}{-2}
=-\frac{2\sqrt{19}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{19}}{2*-1}=\frac{0+4\sqrt{19}}{-2}
=\frac{4\sqrt{19}}{-2}
=\frac{2\sqrt{19}}{-1}
$