3*x^2=1/7

Solution for 3*x^2=1/7 equation:

3*x^2=1/7

We move all terms to the left:

3*x^2-(1/7)=0

We add all the numbers together, and all the variables

3*x^2-(+1/7)=0

We add all the numbers together, and all the variables

3x^2-(+1/7)=0

We get rid of parentheses

3x^2-1/7=0

We multiply all the terms by the denominator


3x^2*7-1=0

Wy multiply elements

21x^2-1=0

a = 21; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·21·(-1)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*21}=\frac{0-2\sqrt{21}}{42}
=-\frac{2\sqrt{21}}{42}
=-\frac{\sqrt{21}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*21}=\frac{0+2\sqrt{21}}{42}
=\frac{2\sqrt{21}}{42}
=\frac{\sqrt{21}}{21}
$