6x^2-13=40

Solution for 6x^2-13=40 equation:

6x^2-13=40

We move all terms to the left:

6x^2-13-(40)=0

We add all the numbers together, and all the variables

6x^2-53=0

a = 6; b = 0; c = -53;
Δ = b2-4ac
Δ = 02-4·6·(-53)
Δ = 1272
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:

$\sqrt{\Delta}=\sqrt{1272}=\sqrt{4*318}=\sqrt{4}*\sqrt{318}=2\sqrt{318}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{318}}{2*6}=\frac{0-2\sqrt{318}}{12}
=-\frac{2\sqrt{318}}{12}
=-\frac{\sqrt{318}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{318}}{2*6}=\frac{0+2\sqrt{318}}{12}
=\frac{2\sqrt{318}}{12}
=\frac{\sqrt{318}}{6}
$