5x^2-6x-22=0

Solution for 5x^2-6x-22=0 equation:

5x^2-6x-22=0

a = 5; b = -6; c = -22;
Δ = b2-4ac
Δ = -62-4·5·(-22)
Δ = 476
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:

$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{119}}{2*5}=\frac{6-2\sqrt{119}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{119}}{2*5}=\frac{6+2\sqrt{119}}{10}
$