6x^2-972=0

Solution for 6x^2-972=0 equation:

6x^2-972=0

a = 6; b = 0; c = -972;
Δ = b2-4ac
Δ = 02-4·6·(-972)
Δ = 23328
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:

$\sqrt{\Delta}=\sqrt{23328}=\sqrt{11664*2}=\sqrt{11664}*\sqrt{2}=108\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-108\sqrt{2}}{2*6}=\frac{0-108\sqrt{2}}{12}
=-\frac{108\sqrt{2}}{12}
=-9\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+108\sqrt{2}}{2*6}=\frac{0+108\sqrt{2}}{12}
=\frac{108\sqrt{2}}{12}
=9\sqrt{2}
$