9x^2+30x-31=0

Solution for 9x^2+30x-31=0 equation:

9x^2+30x-31=0

a = 9; b = 30; c = -31;
Δ = b2-4ac
Δ = 302-4·9·(-31)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{14}}{2*9}=\frac{-30-12\sqrt{14}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{14}}{2*9}=\frac{-30+12\sqrt{14}}{18}
$