3x^2=37.5

Solution for 3x^2=37.5 equation:

3x^2=37.5

We move all terms to the left:

3x^2-(37.5)=0

We add all the numbers together, and all the variables

3x^2-37.5=0

a = 3; b = 0; c = -37.5;
Δ = b2-4ac
Δ = 02-4·3·(-37.5)
Δ = 450
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:

$\sqrt{\Delta}=\sqrt{450}=\sqrt{225*2}=\sqrt{225}*\sqrt{2}=15\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-15\sqrt{2}}{2*3}=\frac{0-15\sqrt{2}}{6}
=-\frac{15\sqrt{2}}{6}
=-\frac{5\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+15\sqrt{2}}{2*3}=\frac{0+15\sqrt{2}}{6}
=\frac{15\sqrt{2}}{6}
=\frac{5\sqrt{2}}{2}
$