8x^2+24x-412=0

Solution for 8x^2+24x-412=0 equation:

8x^2+24x-412=0

a = 8; b = 24; c = -412;
Δ = b2-4ac
Δ = 242-4·8·(-412)
Δ = 13760
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:

$\sqrt{\Delta}=\sqrt{13760}=\sqrt{64*215}=\sqrt{64}*\sqrt{215}=8\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{215}}{2*8}=\frac{-24-8\sqrt{215}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{215}}{2*8}=\frac{-24+8\sqrt{215}}{16}
$