11x^2+204x+288=0

Solution for 11x^2+204x+288=0 equation:

11x^2+204x+288=0

a = 11; b = 204; c = +288;
Δ = b2-4ac
Δ = 2042-4·11·288
Δ = 28944
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:

$\sqrt{\Delta}=\sqrt{28944}=\sqrt{144*201}=\sqrt{144}*\sqrt{201}=12\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(204)-12\sqrt{201}}{2*11}=\frac{-204-12\sqrt{201}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(204)+12\sqrt{201}}{2*11}=\frac{-204+12\sqrt{201}}{22}
$