(x+63)(4x)=180

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

(x+63)(4x)=180

We move all terms to the left:

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

We multiply parentheses

4x^2+252x-180=0

a = 4; b = 252; c = -180;
Δ = b2-4ac
Δ = 2522-4·4·(-180)
Δ = 66384
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:

$\sqrt{\Delta}=\sqrt{66384}=\sqrt{144*461}=\sqrt{144}*\sqrt{461}=12\sqrt{461}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-12\sqrt{461}}{2*4}=\frac{-252-12\sqrt{461}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+12\sqrt{461}}{2*4}=\frac{-252+12\sqrt{461}}{8}
$