-30x^2+31+6=0

Solution for -30x^2+31+6=0 equation:

-30x^2+31+6=0

We add all the numbers together, and all the variables

-30x^2+37=0

a = -30; b = 0; c = +37;
Δ = b2-4ac
Δ = 02-4·(-30)·37
Δ = 4440
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:

$\sqrt{\Delta}=\sqrt{4440}=\sqrt{4*1110}=\sqrt{4}*\sqrt{1110}=2\sqrt{1110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1110}}{2*-30}=\frac{0-2\sqrt{1110}}{-60}
=-\frac{2\sqrt{1110}}{-60}
=-\frac{\sqrt{1110}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1110}}{2*-30}=\frac{0+2\sqrt{1110}}{-60}
=\frac{2\sqrt{1110}}{-60}
=\frac{\sqrt{1110}}{-30}
$