5x2-12x-11=0

Solution for 5x2-12x-11=0 equation:

5x^2-12x-11=0

a = 5; b = -12; c = -11;
Δ = b2-4ac
Δ = -122-4·5·(-11)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{91}}{2*5}=\frac{12-2\sqrt{91}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{91}}{2*5}=\frac{12+2\sqrt{91}}{10}
$