3x^2=513-6

Solution for 3x^2=513-6 equation:

3x^2=513-6

We move all terms to the left:

3x^2-(513-6)=0

We add all the numbers together, and all the variables

3x^2-507=0

a = 3; b = 0; c = -507;
Δ = b2-4ac
Δ = 02-4·3·(-507)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-78}{2*3}=\frac{-78}{6}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+78}{2*3}=\frac{78}{6}
=13
$