11x^2+65x-78=0

Solution for 11x^2+65x-78=0 equation:

11x^2+65x-78=0

a = 11; b = 65; c = -78;
Δ = b2-4ac
Δ = 652-4·11·(-78)
Δ = 7657
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{-(65)-\sqrt{7657}}{2*11}=\frac{-65-\sqrt{7657}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{7657}}{2*11}=\frac{-65+\sqrt{7657}}{22}
$