18x^2=15^5

Solution for 18x^2=15^5 equation:

18x^2=15^5

We move all terms to the left:

18x^2-(15^5)=0

We add all the numbers together, and all the variables

18x^2-759375=0

a = 18; b = 0; c = -759375;
Δ = b2-4ac
Δ = 02-4·18·(-759375)
Δ = 54675000
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:

$\sqrt{\Delta}=\sqrt{54675000}=\sqrt{1822500*30}=\sqrt{1822500}*\sqrt{30}=1350\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1350\sqrt{30}}{2*18}=\frac{0-1350\sqrt{30}}{36}
=-\frac{1350\sqrt{30}}{36}
=-\frac{75\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1350\sqrt{30}}{2*18}=\frac{0+1350\sqrt{30}}{36}
=\frac{1350\sqrt{30}}{36}
=\frac{75\sqrt{30}}{2}
$