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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

y^2-70y=0

a = 1; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·1·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*1}=\frac{0}{2}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*1}=\frac{140}{2}
=70
$