5x^2=150^2

Solution for 5x^2=150^2 equation:

5x^2=150^2

We move all terms to the left:

5x^2-(150^2)=0

We add all the numbers together, and all the variables

5x^2-22500=0

a = 5; b = 0; c = -22500;
Δ = b2-4ac
Δ = 02-4·5·(-22500)
Δ = 450000
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:

$\sqrt{\Delta}=\sqrt{450000}=\sqrt{90000*5}=\sqrt{90000}*\sqrt{5}=300\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300\sqrt{5}}{2*5}=\frac{0-300\sqrt{5}}{10}
=-\frac{300\sqrt{5}}{10}
=-30\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300\sqrt{5}}{2*5}=\frac{0+300\sqrt{5}}{10}
=\frac{300\sqrt{5}}{10}
=30\sqrt{5}
$