x*(4x-3)=180

Solution for x*(4x-3)=180 equation:

x(4x-3)=180

We move all terms to the left:

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

We multiply parentheses

4x^2-3x-180=0

a = 4; b = -3; c = -180;
Δ = b2-4ac
Δ = -32-4·4·(-180)
Δ = 2889
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:

$\sqrt{\Delta}=\sqrt{2889}=\sqrt{9*321}=\sqrt{9}*\sqrt{321}=3\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{321}}{2*4}=\frac{3-3\sqrt{321}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{321}}{2*4}=\frac{3+3\sqrt{321}}{8}
$