1/6m-7=8m-148

Solution for 1/6m-7=8m-148 equation:

1/6m-7=8m-148

We move all terms to the left:

1/6m-7-(8m-148)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R


We get rid of parentheses

1/6m-8m+148-7=0

We multiply all the terms by the denominator


-8m*6m+148*6m-7*6m+1=0

Wy multiply elements

-48m^2+888m-42m+1=0

We add all the numbers together, and all the variables

-48m^2+846m+1=0

a = -48; b = 846; c = +1;
Δ = b2-4ac
Δ = 8462-4·(-48)·1
Δ = 715908
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:

$\sqrt{\Delta}=\sqrt{715908}=\sqrt{4*178977}=\sqrt{4}*\sqrt{178977}=2\sqrt{178977}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(846)-2\sqrt{178977}}{2*-48}=\frac{-846-2\sqrt{178977}}{-96}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(846)+2\sqrt{178977}}{2*-48}=\frac{-846+2\sqrt{178977}}{-96}
$