11x^2-24x-25=0

Solution for 11x^2-24x-25=0 equation:

11x^2-24x-25=0

a = 11; b = -24; c = -25;
Δ = b2-4ac
Δ = -242-4·11·(-25)
Δ = 1676
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:

$\sqrt{\Delta}=\sqrt{1676}=\sqrt{4*419}=\sqrt{4}*\sqrt{419}=2\sqrt{419}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{419}}{2*11}=\frac{24-2\sqrt{419}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{419}}{2*11}=\frac{24+2\sqrt{419}}{22}
$