X(3x-22)+90=180

Solution for X(3x-22)+90=180 equation:

X(3X-22)+90=180

We move all terms to the left:

X(3X-22)+90-(180)=0

We add all the numbers together, and all the variables

X(3X-22)-90=0

We multiply parentheses

3X^2-22X-90=0

a = 3; b = -22; c = -90;
Δ = b2-4ac
Δ = -222-4·3·(-90)
Δ = 1564
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:

$\sqrt{\Delta}=\sqrt{1564}=\sqrt{4*391}=\sqrt{4}*\sqrt{391}=2\sqrt{391}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{391}}{2*3}=\frac{22-2\sqrt{391}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{391}}{2*3}=\frac{22+2\sqrt{391}}{6}
$