6x^2-3=5

Solution for 6x^2-3=5 equation:

6x^2-3=5

We move all terms to the left:

6x^2-3-(5)=0

We add all the numbers together, and all the variables

6x^2-8=0

a = 6; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·6·(-8)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*6}=\frac{0-8\sqrt{3}}{12}
=-\frac{8\sqrt{3}}{12}
=-\frac{2\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*6}=\frac{0+8\sqrt{3}}{12}
=\frac{8\sqrt{3}}{12}
=\frac{2\sqrt{3}}{3}
$