X^2=11x+165

Solution for X^2=11x+165 equation:

X^2=11X+165

We move all terms to the left:

X^2-(11X+165)=0

We get rid of parentheses

X^2-11X-165=0

a = 1; b = -11; c = -165;
Δ = b2-4ac
Δ = -112-4·1·(-165)
Δ = 781
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{781}}{2*1}=\frac{11-\sqrt{781}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{781}}{2*1}=\frac{11+\sqrt{781}}{2}
$