4x^2-31=6

Solution for 4x^2-31=6 equation:

4x^2-31=6

We move all terms to the left:

4x^2-31-(6)=0

We add all the numbers together, and all the variables

4x^2-37=0

a = 4; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·4·(-37)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{37}}{2*4}=\frac{0-4\sqrt{37}}{8}
=-\frac{4\sqrt{37}}{8}
=-\frac{\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{37}}{2*4}=\frac{0+4\sqrt{37}}{8}
=\frac{4\sqrt{37}}{8}
=\frac{\sqrt{37}}{2}
$