4x^2+12x-31=0

Solution for 4x^2+12x-31=0 equation:

4x^2+12x-31=0

a = 4; b = 12; c = -31;
Δ = b2-4ac
Δ = 122-4·4·(-31)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{10}}{2*4}=\frac{-12-8\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{10}}{2*4}=\frac{-12+8\sqrt{10}}{8}
$