7*x^2+16*x-31=0

Solution for 7*x^2+16*x-31=0 equation:

7x^2+16x-31=0

a = 7; b = 16; c = -31;
Δ = b2-4ac
Δ = 162-4·7·(-31)
Δ = 1124
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:

$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{281}}{2*7}=\frac{-16-2\sqrt{281}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{281}}{2*7}=\frac{-16+2\sqrt{281}}{14}
$