2x^2+24x=400

Solution for 2x^2+24x=400 equation:

2x^2+24x=400

We move all terms to the left:

2x^2+24x-(400)=0

a = 2; b = 24; c = -400;
Δ = b2-4ac
Δ = 242-4·2·(-400)
Δ = 3776
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:

$\sqrt{\Delta}=\sqrt{3776}=\sqrt{64*59}=\sqrt{64}*\sqrt{59}=8\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{59}}{2*2}=\frac{-24-8\sqrt{59}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{59}}{2*2}=\frac{-24+8\sqrt{59}}{4}
$