6x*9x=81

Solution for 6x*9x=81 equation:

6x*9x=81

We move all terms to the left:

6x*9x-(81)=0

Wy multiply elements

54x^2-81=0

a = 54; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·54·(-81)
Δ = 17496
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:

$\sqrt{\Delta}=\sqrt{17496}=\sqrt{2916*6}=\sqrt{2916}*\sqrt{6}=54\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54\sqrt{6}}{2*54}=\frac{0-54\sqrt{6}}{108}
=-\frac{54\sqrt{6}}{108}
=-\frac{\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54\sqrt{6}}{2*54}=\frac{0+54\sqrt{6}}{108}
=\frac{54\sqrt{6}}{108}
=\frac{\sqrt{6}}{2}
$