x2+32x+86=0

Solution for x2+32x+86=0 equation:

x2+32x+86=0

We add all the numbers together, and all the variables

x^2+32x+86=0

a = 1; b = 32; c = +86;
Δ = b2-4ac
Δ = 322-4·1·86
Δ = 680
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:

$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{170}}{2*1}=\frac{-32-2\sqrt{170}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{170}}{2*1}=\frac{-32+2\sqrt{170}}{2}
$