3x*2x=78^2

Solution for 3x*2x=78^2 equation:

3x*2x=78^2

We move all terms to the left:

3x*2x-(78^2)=0

We add all the numbers together, and all the variables

3x*2x-6084=0

Wy multiply elements

6x^2-6084=0

a = 6; b = 0; c = -6084;
Δ = b2-4ac
Δ = 02-4·6·(-6084)
Δ = 146016
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:

$\sqrt{\Delta}=\sqrt{146016}=\sqrt{24336*6}=\sqrt{24336}*\sqrt{6}=156\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-156\sqrt{6}}{2*6}=\frac{0-156\sqrt{6}}{12}
=-\frac{156\sqrt{6}}{12}
=-13\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+156\sqrt{6}}{2*6}=\frac{0+156\sqrt{6}}{12}
=\frac{156\sqrt{6}}{12}
=13\sqrt{6}
$