31x^2-150^2=0

Solution for 31x^2-150^2=0 equation:

31x^2-150^2=0

We add all the numbers together, and all the variables

31x^2-22500=0

a = 31; b = 0; c = -22500;
Δ = b2-4ac
Δ = 02-4·31·(-22500)
Δ = 2790000
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:

$\sqrt{\Delta}=\sqrt{2790000}=\sqrt{90000*31}=\sqrt{90000}*\sqrt{31}=300\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300\sqrt{31}}{2*31}=\frac{0-300\sqrt{31}}{62}
=-\frac{300\sqrt{31}}{62}
=-\frac{150\sqrt{31}}{31}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300\sqrt{31}}{2*31}=\frac{0+300\sqrt{31}}{62}
=\frac{300\sqrt{31}}{62}
=\frac{150\sqrt{31}}{31}
$