x^2+8x-83=0

Solution for x^2+8x-83=0 equation:

x^2+8x-83=0

a = 1; b = 8; c = -83;
Δ = b2-4ac
Δ = 82-4·1·(-83)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{11}}{2*1}=\frac{-8-6\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{11}}{2*1}=\frac{-8+6\sqrt{11}}{2}
$