8(3/4m+2)-3(1/6m+-4)=3/2m

Solution for 8(3/4m+2)-3(1/6m+-4)=3/2m equation:

8(3/4m+2)-3(1/6m+-4)=3/2m

We move all terms to the left:

8(3/4m+2)-3(1/6m+-4)-(3/2m)=0


Domain of the equation: 4m+2)!=0

m∈R



Domain of the equation: 6m+-4)!=0

m∈R



Domain of the equation: 2m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

8(3/4m+2)-3(1/6m-4)-(+3/2m)=0

We multiply parentheses

24m-3m-(+3/2m)+16+12=0

We get rid of parentheses

24m-3m-3/2m+16+12=0

We multiply all the terms by the denominator


24m*2m-3m*2m+16*2m+12*2m-3=0

Wy multiply elements

48m^2-6m^2+32m+24m-3=0

We add all the numbers together, and all the variables

42m^2+56m-3=0

a = 42; b = 56; c = -3;
Δ = b2-4ac
Δ = 562-4·42·(-3)
Δ = 3640
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:

$\sqrt{\Delta}=\sqrt{3640}=\sqrt{4*910}=\sqrt{4}*\sqrt{910}=2\sqrt{910}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{910}}{2*42}=\frac{-56-2\sqrt{910}}{84}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{910}}{2*42}=\frac{-56+2\sqrt{910}}{84}
$