3x^2/6=81

Solution for 3x^2/6=81 equation:

3x^2/6=81

We move all terms to the left:

3x^2/6-(81)=0

We multiply all the terms by the denominator


3x^2-81*6=0

We add all the numbers together, and all the variables

3x^2-486=0

a = 3; b = 0; c = -486;
Δ = b2-4ac
Δ = 02-4·3·(-486)
Δ = 5832
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:

$\sqrt{\Delta}=\sqrt{5832}=\sqrt{2916*2}=\sqrt{2916}*\sqrt{2}=54\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54\sqrt{2}}{2*3}=\frac{0-54\sqrt{2}}{6}
=-\frac{54\sqrt{2}}{6}
=-9\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54\sqrt{2}}{2*3}=\frac{0+54\sqrt{2}}{6}
=\frac{54\sqrt{2}}{6}
=9\sqrt{2}
$