5x^2+22x-6=0

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

5x^2+22x-6=0

a = 5; b = 22; c = -6;
Δ = b2-4ac
Δ = 222-4·5·(-6)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{151}}{2*5}=\frac{-22-2\sqrt{151}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{151}}{2*5}=\frac{-22+2\sqrt{151}}{10}
$