4x(3x+1)=180

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

4x(3x+1)=180

We move all terms to the left:

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

We multiply parentheses

12x^2+4x-180=0

a = 12; b = 4; c = -180;
Δ = b2-4ac
Δ = 42-4·12·(-180)
Δ = 8656
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:

$\sqrt{\Delta}=\sqrt{8656}=\sqrt{16*541}=\sqrt{16}*\sqrt{541}=4\sqrt{541}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{541}}{2*12}=\frac{-4-4\sqrt{541}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{541}}{2*12}=\frac{-4+4\sqrt{541}}{24}
$