7/8m+8=7m+2

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

7/8m+8=7m+2

We move all terms to the left:

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


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-56m^2-16m+64m+7=0

We add all the numbers together, and all the variables

-56m^2+48m+7=0

a = -56; b = 48; c = +7;
Δ = b2-4ac
Δ = 482-4·(-56)·7
Δ = 3872
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:

$\sqrt{\Delta}=\sqrt{3872}=\sqrt{1936*2}=\sqrt{1936}*\sqrt{2}=44\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-44\sqrt{2}}{2*-56}=\frac{-48-44\sqrt{2}}{-112}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+44\sqrt{2}}{2*-56}=\frac{-48+44\sqrt{2}}{-112}
$