m=7+1/8m

Solution for m=7+1/8m equation:

m=7+1/8m

We move all terms to the left:

m-(7+1/8m)=0


Domain of the equation: 8m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

m-(1/8m+7)=0

We get rid of parentheses

m-1/8m-7=0

We multiply all the terms by the denominator


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

Wy multiply elements

8m^2-56m-1=0

a = 8; b = -56; c = -1;
Δ = b2-4ac
Δ = -562-4·8·(-1)
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-12\sqrt{22}}{2*8}=\frac{56-12\sqrt{22}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+12\sqrt{22}}{2*8}=\frac{56+12\sqrt{22}}{16}
$