15=1/5x^2

Solution for 15=1/5x^2 equation:

15=1/5x^2

We move all terms to the left:

15-(1/5x^2)=0


Domain of the equation: 5x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/5x^2+15=0

We multiply all the terms by the denominator


15*5x^2-1=0

Wy multiply elements

75x^2-1=0

a = 75; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·75·(-1)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*75}=\frac{0-10\sqrt{3}}{150}
=-\frac{10\sqrt{3}}{150}
=-\frac{\sqrt{3}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*75}=\frac{0+10\sqrt{3}}{150}
=\frac{10\sqrt{3}}{150}
=\frac{\sqrt{3}}{15}
$