x^2-30+11x=180

Solution for x^2-30+11x=180 equation:

x^2-30+11x=180

We move all terms to the left:

x^2-30+11x-(180)=0

We add all the numbers together, and all the variables

x^2+11x-210=0

a = 1; b = 11; c = -210;
Δ = b2-4ac
Δ = 112-4·1·(-210)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-31}{2*1}=\frac{-42}{2}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+31}{2*1}=\frac{20}{2}
=10
$