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

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

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

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3m+1/2m-4m+8=0

We multiply all the terms by the denominator


3m*2m-4m*2m+8*2m+1=0

Wy multiply elements

6m^2-8m^2+16m+1=0

We add all the numbers together, and all the variables

-2m^2+16m+1=0

a = -2; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·(-2)·1
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{66}}{2*-2}=\frac{-16-2\sqrt{66}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{66}}{2*-2}=\frac{-16+2\sqrt{66}}{-4}
$