(x+25)(2x-4)+63=180

Solution for (x+25)(2x-4)+63=180 equation:

(x+25)(2x-4)+63=180

We move all terms to the left:

(x+25)(2x-4)+63-(180)=0

We add all the numbers together, and all the variables

(x+25)(2x-4)-117=0

We multiply parentheses ..

(+2x^2-4x+50x-100)-117=0

We get rid of parentheses

2x^2-4x+50x-100-117=0

We add all the numbers together, and all the variables

2x^2+46x-217=0

a = 2; b = 46; c = -217;
Δ = b2-4ac
Δ = 462-4·2·(-217)
Δ = 3852
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:

$\sqrt{\Delta}=\sqrt{3852}=\sqrt{36*107}=\sqrt{36}*\sqrt{107}=6\sqrt{107}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-6\sqrt{107}}{2*2}=\frac{-46-6\sqrt{107}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+6\sqrt{107}}{2*2}=\frac{-46+6\sqrt{107}}{4}
$