340^2=6x2

Solution for 340^2=6x2 equation:

340^2=6x^2

We move all terms to the left:

340^2-(6x^2)=0

We add all the numbers together, and all the variables

-6x^2+115600=0

a = -6; b = 0; c = +115600;
Δ = b2-4ac
Δ = 02-4·(-6)·115600
Δ = 2774400
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:

$\sqrt{\Delta}=\sqrt{2774400}=\sqrt{462400*6}=\sqrt{462400}*\sqrt{6}=680\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-680\sqrt{6}}{2*-6}=\frac{0-680\sqrt{6}}{-12}
=-\frac{680\sqrt{6}}{-12}
=-\frac{170\sqrt{6}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+680\sqrt{6}}{2*-6}=\frac{0+680\sqrt{6}}{-12}
=\frac{680\sqrt{6}}{-12}
=\frac{170\sqrt{6}}{-3}
$