11x^2+112x-65=0

Solution for 11x^2+112x-65=0 equation:

11x^2+112x-65=0

a = 11; b = 112; c = -65;
Δ = b2-4ac
Δ = 1122-4·11·(-65)
Δ = 15404
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:

$\sqrt{\Delta}=\sqrt{15404}=\sqrt{4*3851}=\sqrt{4}*\sqrt{3851}=2\sqrt{3851}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-2\sqrt{3851}}{2*11}=\frac{-112-2\sqrt{3851}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+2\sqrt{3851}}{2*11}=\frac{-112+2\sqrt{3851}}{22}
$