3780-(90-2x)(42-2x)=720

Solution for 3780-(90-2x)(42-2x)=720 equation:

3780-(90-2x)(42-2x)=720

We move all terms to the left:

3780-(90-2x)(42-2x)-(720)=0

We add all the numbers together, and all the variables

-(-2x+90)(-2x+42)+3780-720=0

We add all the numbers together, and all the variables

-(-2x+90)(-2x+42)+3060=0

We multiply parentheses ..

-(+4x^2-84x-180x+3780)+3060=0

We get rid of parentheses

-4x^2+84x+180x-3780+3060=0

We add all the numbers together, and all the variables

-4x^2+264x-720=0

a = -4; b = 264; c = -720;
Δ = b2-4ac
Δ = 2642-4·(-4)·(-720)
Δ = 58176
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:

$\sqrt{\Delta}=\sqrt{58176}=\sqrt{576*101}=\sqrt{576}*\sqrt{101}=24\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(264)-24\sqrt{101}}{2*-4}=\frac{-264-24\sqrt{101}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(264)+24\sqrt{101}}{2*-4}=\frac{-264+24\sqrt{101}}{-8}
$