(10-y)(60+y)=600

Solution for (10-y)(60+y)=600 equation:

(10-y)(60+y)=600

We move all terms to the left:

(10-y)(60+y)-(600)=0

We add all the numbers together, and all the variables

(-1y+10)(y+60)-600=0

We multiply parentheses ..

(-1y^2-60y+10y+600)-600=0

We get rid of parentheses

-1y^2-60y+10y+600-600=0

We add all the numbers together, and all the variables

-1y^2-50y=0

a = -1; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·(-1)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*-1}=\frac{0}{-2}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*-1}=\frac{100}{-2}
=-50
$