1/3x^2=19

Solution for 1/3x^2=19 equation:

1/3x^2=19

We move all terms to the left:

1/3x^2-(19)=0


Domain of the equation: 3x^2!=0

x^2!=0/3

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-19*3x^2+1=0

Wy multiply elements

-57x^2+1=0

a = -57; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-57)·1
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{57}}{2*-57}=\frac{0-2\sqrt{57}}{-114}
=-\frac{2\sqrt{57}}{-114}
=-\frac{\sqrt{57}}{-57}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{57}}{2*-57}=\frac{0+2\sqrt{57}}{-114}
=\frac{2\sqrt{57}}{-114}
=\frac{\sqrt{57}}{-57}
$