1/3x2-14=9

Solution for 1/3x2-14=9 equation:

1/3x^2-14=9

We move all terms to the left:

1/3x^2-14-(9)=0


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

x^2!=0/3

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x^2-23=0

We multiply all the terms by the denominator


-23*3x^2+1=0

Wy multiply elements

-69x^2+1=0

a = -69; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-69)·1
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{69}}{2*-69}=\frac{0-2\sqrt{69}}{-138}
=-\frac{2\sqrt{69}}{-138}
=-\frac{\sqrt{69}}{-69}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{69}}{2*-69}=\frac{0+2\sqrt{69}}{-138}
=\frac{2\sqrt{69}}{-138}
=\frac{\sqrt{69}}{-69}
$