6x^2=510

Solution for 6x^2=510 equation:

6x^2=510

We move all terms to the left:

6x^2-(510)=0

a = 6; b = 0; c = -510;
Δ = b2-4ac
Δ = 02-4·6·(-510)
Δ = 12240
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:

$\sqrt{\Delta}=\sqrt{12240}=\sqrt{144*85}=\sqrt{144}*\sqrt{85}=12\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{85}}{2*6}=\frac{0-12\sqrt{85}}{12}
=-\frac{12\sqrt{85}}{12}
=-\sqrt{85}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{85}}{2*6}=\frac{0+12\sqrt{85}}{12}
=\frac{12\sqrt{85}}{12}
=\sqrt{85}
$