(X+45)(2x-2)=180

Solution for (X+45)(2x-2)=180 equation:

(X+45)(2X-2)=180

We move all terms to the left:

(X+45)(2X-2)-(180)=0

We multiply parentheses ..

(+2X^2-2X+90X-90)-180=0

We get rid of parentheses

2X^2-2X+90X-90-180=0

We add all the numbers together, and all the variables

2X^2+88X-270=0

a = 2; b = 88; c = -270;
Δ = b2-4ac
Δ = 882-4·2·(-270)
Δ = 9904
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:

$\sqrt{\Delta}=\sqrt{9904}=\sqrt{16*619}=\sqrt{16}*\sqrt{619}=4\sqrt{619}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-4\sqrt{619}}{2*2}=\frac{-88-4\sqrt{619}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+4\sqrt{619}}{2*2}=\frac{-88+4\sqrt{619}}{4}
$