1/3x^2-32=17

Solution for 1/3x^2-32=17 equation:

1/3x^2-32=17

We move all terms to the left:

1/3x^2-32-(17)=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^2-49=0

We multiply all the terms by the denominator


-49*3x^2+1=0

Wy multiply elements

-147x^2+1=0

a = -147; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-147)·1
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{3}}{2*-147}=\frac{0-14\sqrt{3}}{-294}
=-\frac{14\sqrt{3}}{-294}
=-\frac{\sqrt{3}}{-21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*-147}=\frac{0+14\sqrt{3}}{-294}
=\frac{14\sqrt{3}}{-294}
=\frac{\sqrt{3}}{-21}
$