6-8m^2=1/3

Solution for 6-8m^2=1/3 equation:

6-8m^2=1/3

We move all terms to the left:

6-8m^2-(1/3)=0

We add all the numbers together, and all the variables

-8m^2+6-(+1/3)=0

We get rid of parentheses

-8m^2+6-1/3=0

We multiply all the terms by the denominator


-8m^2*3-1+6*3=0

We add all the numbers together, and all the variables

-8m^2*3+17=0

Wy multiply elements

-24m^2+17=0

a = -24; b = 0; c = +17;
Δ = b2-4ac
Δ = 02-4·(-24)·17
Δ = 1632
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{102}}{2*-24}=\frac{0-4\sqrt{102}}{-48}
=-\frac{4\sqrt{102}}{-48}
=-\frac{\sqrt{102}}{-12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{102}}{2*-24}=\frac{0+4\sqrt{102}}{-48}
=\frac{4\sqrt{102}}{-48}
=\frac{\sqrt{102}}{-12}
$