(40-2x)(60-2x)=1500

Solution for (40-2x)(60-2x)=1500 equation:

(40-2x)(60-2x)=1500

We move all terms to the left:

(40-2x)(60-2x)-(1500)=0

We add all the numbers together, and all the variables

(-2x+40)(-2x+60)-1500=0

We multiply parentheses ..

(+4x^2-120x-80x+2400)-1500=0

We get rid of parentheses

4x^2-120x-80x+2400-1500=0

We add all the numbers together, and all the variables

4x^2-200x+900=0

a = 4; b = -200; c = +900;
Δ = b2-4ac
Δ = -2002-4·4·900
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-160}{2*4}=\frac{40}{8}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+160}{2*4}=\frac{360}{8}
=45
$