2x^2+24x=-71

Solution for 2x^2+24x=-71 equation:

2x^2+24x=-71

We move all terms to the left:

2x^2+24x-(-71)=0

We add all the numbers together, and all the variables

2x^2+24x+71=0

a = 2; b = 24; c = +71;
Δ = b2-4ac
Δ = 242-4·2·71
Δ = 8
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:

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