90+2x(3x-10)=180

Solution for 90+2x(3x-10)=180 equation:

90+2x(3x-10)=180

We move all terms to the left:

90+2x(3x-10)-(180)=0

We add all the numbers together, and all the variables

2x(3x-10)-90=0

We multiply parentheses

6x^2-20x-90=0

a = 6; b = -20; c = -90;
Δ = b2-4ac
Δ = -202-4·6·(-90)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16\sqrt{10}}{2*6}=\frac{20-16\sqrt{10}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16\sqrt{10}}{2*6}=\frac{20+16\sqrt{10}}{12}
$