11x^2+121x+308=90

Solution for 11x^2+121x+308=90 equation:

11x^2+121x+308=90

We move all terms to the left:

11x^2+121x+308-(90)=0

We add all the numbers together, and all the variables

11x^2+121x+218=0

a = 11; b = 121; c = +218;
Δ = b2-4ac
Δ = 1212-4·11·218
Δ = 5049
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:

$\sqrt{\Delta}=\sqrt{5049}=\sqrt{9*561}=\sqrt{9}*\sqrt{561}=3\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(121)-3\sqrt{561}}{2*11}=\frac{-121-3\sqrt{561}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+3\sqrt{561}}{2*11}=\frac{-121+3\sqrt{561}}{22}
$