3x^2=9^8

Solution for 3x^2=9^8 equation:

3x^2=9^8

We move all terms to the left:

3x^2-(9^8)=0

We add all the numbers together, and all the variables

3x^2-43046721=0

a = 3; b = 0; c = -43046721;
Δ = b2-4ac
Δ = 02-4·3·(-43046721)
Δ = 516560652
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:

$\sqrt{\Delta}=\sqrt{516560652}=\sqrt{172186884*3}=\sqrt{172186884}*\sqrt{3}=13122\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-13122\sqrt{3}}{2*3}=\frac{0-13122\sqrt{3}}{6}
=-\frac{13122\sqrt{3}}{6}
=-2187\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+13122\sqrt{3}}{2*3}=\frac{0+13122\sqrt{3}}{6}
=\frac{13122\sqrt{3}}{6}
=2187\sqrt{3}
$