100=3x^2+7

Solution for 100=3x^2+7 equation:

100=3x^2+7

We move all terms to the left:

100-(3x^2+7)=0

We get rid of parentheses

-3x^2-7+100=0

We add all the numbers together, and all the variables

-3x^2+93=0

a = -3; b = 0; c = +93;
Δ = b2-4ac
Δ = 02-4·(-3)·93
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{31}}{2*-3}=\frac{0-6\sqrt{31}}{-6}
=-\frac{6\sqrt{31}}{-6}
=-\frac{\sqrt{31}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{31}}{2*-3}=\frac{0+6\sqrt{31}}{-6}
=\frac{6\sqrt{31}}{-6}
=\frac{\sqrt{31}}{-1}
$