2a2+24a-64=0

Solution for 2a2+24a-64=0 equation:

2a^2+24a-64=0

a = 2; b = 24; c = -64;
Δ = b2-4ac
Δ = 242-4·2·(-64)
Δ = 1088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{17}}{2*2}=\frac{-24-8\sqrt{17}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{17}}{2*2}=\frac{-24+8\sqrt{17}}{4}
$