3x^2=22.5

Solution for 3x^2=22.5 equation:

3x^2=22.5

We move all terms to the left:

3x^2-(22.5)=0

We add all the numbers together, and all the variables

3x^2-22.5=0

a = 3; b = 0; c = -22.5;
Δ = b2-4ac
Δ = 02-4·3·(-22.5)
Δ = 270
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:

$\sqrt{\Delta}=\sqrt{270}=\sqrt{9*30}=\sqrt{9}*\sqrt{30}=3\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{30}}{2*3}=\frac{0-3\sqrt{30}}{6}
=-\frac{3\sqrt{30}}{6}
=-\frac{\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{30}}{2*3}=\frac{0+3\sqrt{30}}{6}
=\frac{3\sqrt{30}}{6}
=\frac{\sqrt{30}}{2}
$