3x^2-7=533

Solution for 3x^2-7=533 equation:

3x^2-7=533

We move all terms to the left:

3x^2-7-(533)=0

We add all the numbers together, and all the variables

3x^2-540=0

a = 3; b = 0; c = -540;
Δ = b2-4ac
Δ = 02-4·3·(-540)
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{5}}{2*3}=\frac{0-36\sqrt{5}}{6}
=-\frac{36\sqrt{5}}{6}
=-6\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{5}}{2*3}=\frac{0+36\sqrt{5}}{6}
=\frac{36\sqrt{5}}{6}
=6\sqrt{5}
$