2x^2-48=780

Solution for 2x^2-48=780 equation:

2x^2-48=780

We move all terms to the left:

2x^2-48-(780)=0

We add all the numbers together, and all the variables

2x^2-828=0

a = 2; b = 0; c = -828;
Δ = b2-4ac
Δ = 02-4·2·(-828)
Δ = 6624
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:

$\sqrt{\Delta}=\sqrt{6624}=\sqrt{144*46}=\sqrt{144}*\sqrt{46}=12\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{46}}{2*2}=\frac{0-12\sqrt{46}}{4}
=-\frac{12\sqrt{46}}{4}
=-3\sqrt{46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{46}}{2*2}=\frac{0+12\sqrt{46}}{4}
=\frac{12\sqrt{46}}{4}
=3\sqrt{46}
$