(4x)(3x+47)+63=180

Solution for (4x)(3x+47)+63=180 equation:

(4x)(3x+47)+63=180

We move all terms to the left:

(4x)(3x+47)+63-(180)=0

We add all the numbers together, and all the variables

4x(3x+47)-117=0

We multiply parentheses

12x^2+188x-117=0

a = 12; b = 188; c = -117;
Δ = b2-4ac
Δ = 1882-4·12·(-117)
Δ = 40960
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:

$\sqrt{\Delta}=\sqrt{40960}=\sqrt{4096*10}=\sqrt{4096}*\sqrt{10}=64\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(188)-64\sqrt{10}}{2*12}=\frac{-188-64\sqrt{10}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(188)+64\sqrt{10}}{2*12}=\frac{-188+64\sqrt{10}}{24}
$