24=6x^2-10

Solution for 24=6x^2-10 equation:

24=6x^2-10

We move all terms to the left:

24-(6x^2-10)=0

We get rid of parentheses

-6x^2+10+24=0

We add all the numbers together, and all the variables

-6x^2+34=0

a = -6; b = 0; c = +34;
Δ = b2-4ac
Δ = 02-4·(-6)·34
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{51}}{2*-6}=\frac{0-4\sqrt{51}}{-12}
=-\frac{4\sqrt{51}}{-12}
=-\frac{\sqrt{51}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{51}}{2*-6}=\frac{0+4\sqrt{51}}{-12}
=\frac{4\sqrt{51}}{-12}
=\frac{\sqrt{51}}{-3}
$