2x^2+6x-48=576

Solution for 2x^2+6x-48=576 equation:

2x^2+6x-48=576

We move all terms to the left:

2x^2+6x-48-(576)=0

We add all the numbers together, and all the variables

2x^2+6x-624=0

a = 2; b = 6; c = -624;
Δ = b2-4ac
Δ = 62-4·2·(-624)
Δ = 5028
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:

$\sqrt{\Delta}=\sqrt{5028}=\sqrt{4*1257}=\sqrt{4}*\sqrt{1257}=2\sqrt{1257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{1257}}{2*2}=\frac{-6-2\sqrt{1257}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{1257}}{2*2}=\frac{-6+2\sqrt{1257}}{4}
$