(40-2x)(30-2x)=900

Solution for (40-2x)(30-2x)=900 equation:

(40-2x)(30-2x)=900

We move all terms to the left:

(40-2x)(30-2x)-(900)=0

We add all the numbers together, and all the variables

(-2x+40)(-2x+30)-900=0

We multiply parentheses ..

(+4x^2-60x-80x+1200)-900=0

We get rid of parentheses

4x^2-60x-80x+1200-900=0

We add all the numbers together, and all the variables

4x^2-140x+300=0

a = 4; b = -140; c = +300;
Δ = b2-4ac
Δ = -1402-4·4·300
Δ = 14800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14800}=\sqrt{400*37}=\sqrt{400}*\sqrt{37}=20\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-20\sqrt{37}}{2*4}=\frac{140-20\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+20\sqrt{37}}{2*4}=\frac{140+20\sqrt{37}}{8}
$