10/m+18-7/8m=3/8m+25

Solution for 10/m+18-7/8m=3/8m+25 equation:

10/m+18-7/8m=3/8m+25

We move all terms to the left:

10/m+18-7/8m-(3/8m+25)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R



Domain of the equation: 8m+25)!=0

m∈R


We get rid of parentheses

10/m-7/8m-3/8m-25+18=0

We calculate fractions


80m/8m^2+(-3m-7)/8m^2-25+18=0

We add all the numbers together, and all the variables

80m/8m^2+(-3m-7)/8m^2-7=0

We multiply all the terms by the denominator


80m+(-3m-7)-7*8m^2=0

Wy multiply elements

-56m^2+80m+(-3m-7)=0

We get rid of parentheses

-56m^2+80m-3m-7=0

We add all the numbers together, and all the variables

-56m^2+77m-7=0

a = -56; b = 77; c = -7;
Δ = b2-4ac
Δ = 772-4·(-56)·(-7)
Δ = 4361
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:

$\sqrt{\Delta}=\sqrt{4361}=\sqrt{49*89}=\sqrt{49}*\sqrt{89}=7\sqrt{89}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-7\sqrt{89}}{2*-56}=\frac{-77-7\sqrt{89}}{-112}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+7\sqrt{89}}{2*-56}=\frac{-77+7\sqrt{89}}{-112}
$