-4x^2+8x+86=0

Solution for -4x^2+8x+86=0 equation:

-4x^2+8x+86=0

a = -4; b = 8; c = +86;
Δ = b2-4ac
Δ = 82-4·(-4)·86
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{10}}{2*-4}=\frac{-8-12\sqrt{10}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{10}}{2*-4}=\frac{-8+12\sqrt{10}}{-8}
$