4x(3x+1)=180-23

Solution for 4x(3x+1)=180-23 equation:

4x(3x+1)=180-23

We move all terms to the left:

4x(3x+1)-(180-23)=0

We add all the numbers together, and all the variables

4x(3x+1)-157=0

We multiply parentheses

12x^2+4x-157=0

a = 12; b = 4; c = -157;
Δ = b2-4ac
Δ = 42-4·12·(-157)
Δ = 7552
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:

$\sqrt{\Delta}=\sqrt{7552}=\sqrt{64*118}=\sqrt{64}*\sqrt{118}=8\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{118}}{2*12}=\frac{-4-8\sqrt{118}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{118}}{2*12}=\frac{-4+8\sqrt{118}}{24}
$