2x(x-3)+90=180

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

2x(x-3)+90=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x(x-3)-90=0

We multiply parentheses

2x^2-6x-90=0

a = 2; b = -6; c = -90;
Δ = b2-4ac
Δ = -62-4·2·(-90)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{21}}{2*2}=\frac{6-6\sqrt{21}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{21}}{2*2}=\frac{6+6\sqrt{21}}{4}
$