x(4x-3)+90=180

Solution for x(4x-3)+90=180 equation:

x(4x-3)+90=180

We move all terms to the left:

x(4x-3)+90-(180)=0

We add all the numbers together, and all the variables

x(4x-3)-90=0

We multiply parentheses

4x^2-3x-90=0

a = 4; b = -3; c = -90;
Δ = b2-4ac
Δ = -32-4·4·(-90)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{161}}{2*4}=\frac{3-3\sqrt{161}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{161}}{2*4}=\frac{3+3\sqrt{161}}{8}
$