-6x2=-414

Solution for -6x2=-414 equation:

-6x^2=-414

We move all terms to the left:

-6x^2-(-414)=0

We add all the numbers together, and all the variables

-6x^2+414=0

a = -6; b = 0; c = +414;
Δ = b2-4ac
Δ = 02-4·(-6)·414
Δ = 9936
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:

$\sqrt{\Delta}=\sqrt{9936}=\sqrt{144*69}=\sqrt{144}*\sqrt{69}=12\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{69}}{2*-6}=\frac{0-12\sqrt{69}}{-12}
=-\frac{12\sqrt{69}}{-12}
=-\frac{\sqrt{69}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{69}}{2*-6}=\frac{0+12\sqrt{69}}{-12}
=\frac{12\sqrt{69}}{-12}
=\frac{\sqrt{69}}{-1}
$