4x^2=972

Solution for 4x^2=972 equation:

4x^2=972

We move all terms to the left:

4x^2-(972)=0

a = 4; b = 0; c = -972;
Δ = b2-4ac
Δ = 02-4·4·(-972)
Δ = 15552
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:

$\sqrt{\Delta}=\sqrt{15552}=\sqrt{5184*3}=\sqrt{5184}*\sqrt{3}=72\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{3}}{2*4}=\frac{0-72\sqrt{3}}{8}
=-\frac{72\sqrt{3}}{8}
=-9\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{3}}{2*4}=\frac{0+72\sqrt{3}}{8}
=\frac{72\sqrt{3}}{8}
=9\sqrt{3}
$