6x^2-10=30

Solution for 6x^2-10=30 equation:

6x^2-10=30

We move all terms to the left:

6x^2-10-(30)=0

We add all the numbers together, and all the variables

6x^2-40=0

a = 6; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·6·(-40)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*6}=\frac{0-8\sqrt{15}}{12}
=-\frac{8\sqrt{15}}{12}
=-\frac{2\sqrt{15}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*6}=\frac{0+8\sqrt{15}}{12}
=\frac{8\sqrt{15}}{12}
=\frac{2\sqrt{15}}{3}
$