(5x^2)/3=9^4

Solution for (5x^2)/3=9^4 equation:

(5x^2)/3=9^4

We move all terms to the left:

(5x^2)/3-(9^4)=0

We add all the numbers together, and all the variables

5x^2/3-6561=0

We multiply all the terms by the denominator


5x^2-6561*3=0

We add all the numbers together, and all the variables

5x^2-19683=0

a = 5; b = 0; c = -19683;
Δ = b2-4ac
Δ = 02-4·5·(-19683)
Δ = 393660
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:

$\sqrt{\Delta}=\sqrt{393660}=\sqrt{26244*15}=\sqrt{26244}*\sqrt{15}=162\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-162\sqrt{15}}{2*5}=\frac{0-162\sqrt{15}}{10}
=-\frac{162\sqrt{15}}{10}
=-\frac{81\sqrt{15}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+162\sqrt{15}}{2*5}=\frac{0+162\sqrt{15}}{10}
=\frac{162\sqrt{15}}{10}
=\frac{81\sqrt{15}}{5}
$