3x^2-22x-31=0

Solution for 3x^2-22x-31=0 equation:

3x^2-22x-31=0

a = 3; b = -22; c = -31;
Δ = b2-4ac
Δ = -222-4·3·(-31)
Δ = 856
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:

$\sqrt{\Delta}=\sqrt{856}=\sqrt{4*214}=\sqrt{4}*\sqrt{214}=2\sqrt{214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{214}}{2*3}=\frac{22-2\sqrt{214}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{214}}{2*3}=\frac{22+2\sqrt{214}}{6}
$