2x2+8x=216

Solution for 2x2+8x=216 equation:

2x^2+8x=216

We move all terms to the left:

2x^2+8x-(216)=0

a = 2; b = 8; c = -216;
Δ = b2-4ac
Δ = 82-4·2·(-216)
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{7}}{2*2}=\frac{-8-16\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{7}}{2*2}=\frac{-8+16\sqrt{7}}{4}
$