6-3x^2=-117

Solution for 6-3x^2=-117 equation:

6-3x^2=-117

We move all terms to the left:

6-3x^2-(-117)=0

We add all the numbers together, and all the variables

-3x^2+123=0

a = -3; b = 0; c = +123;
Δ = b2-4ac
Δ = 02-4·(-3)·123
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{41}}{2*-3}=\frac{0-6\sqrt{41}}{-6}
=-\frac{6\sqrt{41}}{-6}
=-\frac{\sqrt{41}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{41}}{2*-3}=\frac{0+6\sqrt{41}}{-6}
=\frac{6\sqrt{41}}{-6}
=\frac{\sqrt{41}}{-1}
$