5x(3x-4)+90=180

Solution for 5x(3x-4)+90=180 equation:

5x(3x-4)+90=180

We move all terms to the left:

5x(3x-4)+90-(180)=0

We add all the numbers together, and all the variables

5x(3x-4)-90=0

We multiply parentheses

15x^2-20x-90=0

a = 15; b = -20; c = -90;
Δ = b2-4ac
Δ = -202-4·15·(-90)
Δ = 5800
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:

$\sqrt{\Delta}=\sqrt{5800}=\sqrt{100*58}=\sqrt{100}*\sqrt{58}=10\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{58}}{2*15}=\frac{20-10\sqrt{58}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{58}}{2*15}=\frac{20+10\sqrt{58}}{30}
$