18x^2-31=0

Solution for 18x^2-31=0 equation:

18x^2-31=0

a = 18; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·18·(-31)
Δ = 2232
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:

$\sqrt{\Delta}=\sqrt{2232}=\sqrt{36*62}=\sqrt{36}*\sqrt{62}=6\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{62}}{2*18}=\frac{0-6\sqrt{62}}{36}
=-\frac{6\sqrt{62}}{36}
=-\frac{\sqrt{62}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{62}}{2*18}=\frac{0+6\sqrt{62}}{36}
=\frac{6\sqrt{62}}{36}
=\frac{\sqrt{62}}{6}
$