9x^2-2=457

Solution for 9x^2-2=457 equation:

9x^2-2=457

We move all terms to the left:

9x^2-2-(457)=0

We add all the numbers together, and all the variables

9x^2-459=0

a = 9; b = 0; c = -459;
Δ = b2-4ac
Δ = 02-4·9·(-459)
Δ = 16524
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:

$\sqrt{\Delta}=\sqrt{16524}=\sqrt{324*51}=\sqrt{324}*\sqrt{51}=18\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{51}}{2*9}=\frac{0-18\sqrt{51}}{18}
=-\frac{18\sqrt{51}}{18}
=-\sqrt{51}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{51}}{2*9}=\frac{0+18\sqrt{51}}{18}
=\frac{18\sqrt{51}}{18}
=\sqrt{51}
$