2x^2+6x-31=0

Solution for 2x^2+6x-31=0 equation:

2x^2+6x-31=0

a = 2; b = 6; c = -31;
Δ = b2-4ac
Δ = 62-4·2·(-31)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{71}}{2*2}=\frac{-6-2\sqrt{71}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{71}}{2*2}=\frac{-6+2\sqrt{71}}{4}
$