7/8m-2=m

Solution for 7/8m-2=m equation:

7/8m-2=m

We move all terms to the left:

7/8m-2-(m)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R


We add all the numbers together, and all the variables

-1m+7/8m-2=0

We multiply all the terms by the denominator


-1m*8m-2*8m+7=0

Wy multiply elements

-8m^2-16m+7=0

a = -8; b = -16; c = +7;
Δ = b2-4ac
Δ = -162-4·(-8)·7
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{30}}{2*-8}=\frac{16-4\sqrt{30}}{-16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{30}}{2*-8}=\frac{16+4\sqrt{30}}{-16}
$