3/4m+8=1/2m-2

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Solution for 3/4m+8=1/2m-2 equation:



3/4m+8=1/2m-2
We move all terms to the left:
3/4m+8-(1/2m-2)=0
Domain of the equation: 4m!=0
m!=0/4
m!=0
m∈R
Domain of the equation: 2m-2)!=0
m∈R
We get rid of parentheses
3/4m-1/2m+2+8=0
We calculate fractions
6m/8m^2+(-4m)/8m^2+2+8=0
We add all the numbers together, and all the variables
6m/8m^2+(-4m)/8m^2+10=0
We multiply all the terms by the denominator
6m+(-4m)+10*8m^2=0
Wy multiply elements
80m^2+6m+(-4m)=0
We get rid of parentheses
80m^2+6m-4m=0
We add all the numbers together, and all the variables
80m^2+2m=0
a = 80; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·80·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*80}=\frac{-4}{160} =-1/40 $
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*80}=\frac{0}{160} =0 $

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