6=5x^2-2

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

6=5x^2-2

We move all terms to the left:

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

We get rid of parentheses

-5x^2+2+6=0

We add all the numbers together, and all the variables

-5x^2+8=0

a = -5; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-5)·8
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*-5}=\frac{0-4\sqrt{10}}{-10}
=-\frac{4\sqrt{10}}{-10}
=-\frac{2\sqrt{10}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*-5}=\frac{0+4\sqrt{10}}{-10}
=\frac{4\sqrt{10}}{-10}
=\frac{2\sqrt{10}}{-5}
$