5x2-10x-11=0

Solution for 5x2-10x-11=0 equation:

5x^2-10x-11=0

a = 5; b = -10; c = -11;
Δ = b2-4ac
Δ = -102-4·5·(-11)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8\sqrt{5}}{2*5}=\frac{10-8\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8\sqrt{5}}{2*5}=\frac{10+8\sqrt{5}}{10}
$