8x^2+24x-78=0

Solution for 8x^2+24x-78=0 equation:

8x^2+24x-78=0

a = 8; b = 24; c = -78;
Δ = b2-4ac
Δ = 242-4·8·(-78)
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-32\sqrt{3}}{2*8}=\frac{-24-32\sqrt{3}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+32\sqrt{3}}{2*8}=\frac{-24+32\sqrt{3}}{16}
$