3x^2-2=288

Solution for 3x^2-2=288 equation:

3x^2-2=288

We move all terms to the left:

3x^2-2-(288)=0

We add all the numbers together, and all the variables

3x^2-290=0

a = 3; b = 0; c = -290;
Δ = b2-4ac
Δ = 02-4·3·(-290)
Δ = 3480
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:

$\sqrt{\Delta}=\sqrt{3480}=\sqrt{4*870}=\sqrt{4}*\sqrt{870}=2\sqrt{870}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{870}}{2*3}=\frac{0-2\sqrt{870}}{6}
=-\frac{2\sqrt{870}}{6}
=-\frac{\sqrt{870}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{870}}{2*3}=\frac{0+2\sqrt{870}}{6}
=\frac{2\sqrt{870}}{6}
=\frac{\sqrt{870}}{3}
$