6532=6x^2

Solution for 6532=6x^2 equation:

6532=6x^2

We move all terms to the left:

6532-(6x^2)=0

a = -6; b = 0; c = +6532;
Δ = b2-4ac
Δ = 02-4·(-6)·6532
Δ = 156768
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:

$\sqrt{\Delta}=\sqrt{156768}=\sqrt{16*9798}=\sqrt{16}*\sqrt{9798}=4\sqrt{9798}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{9798}}{2*-6}=\frac{0-4\sqrt{9798}}{-12}
=-\frac{4\sqrt{9798}}{-12}
=-\frac{\sqrt{9798}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{9798}}{2*-6}=\frac{0+4\sqrt{9798}}{-12}
=\frac{4\sqrt{9798}}{-12}
=\frac{\sqrt{9798}}{-3}
$