(45-2x)(35-2x)=900

Solution for (45-2x)(35-2x)=900 equation:

(45-2x)(35-2x)=900

We move all terms to the left:

(45-2x)(35-2x)-(900)=0

We add all the numbers together, and all the variables

(-2x+45)(-2x+35)-900=0

We multiply parentheses ..

(+4x^2-70x-90x+1575)-900=0

We get rid of parentheses

4x^2-70x-90x+1575-900=0

We add all the numbers together, and all the variables

4x^2-160x+675=0

a = 4; b = -160; c = +675;
Δ = b2-4ac
Δ = -1602-4·4·675
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{-(-160)-20\sqrt{37}}{2*4}=\frac{160-20\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+20\sqrt{37}}{2*4}=\frac{160+20\sqrt{37}}{8}
$