14m-7-1/2m=2-1.5m

Solution for 14m-7-1/2m=2-1.5m equation:

14m-7-1/2m=2-1.5m

We move all terms to the left:

14m-7-1/2m-(2-1.5m)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

14m-1/2m-(-1.5m+2)-7=0

We get rid of parentheses

14m-1/2m+1.5m-2-7=0

We multiply all the terms by the denominator


14m*2m+(1.5m)*2m-2*2m-7*2m-1=0

We add all the numbers together, and all the variables

14m*2m+(+1.5m)*2m-2*2m-7*2m-1=0

We multiply parentheses

2m^2+14m*2m-2*2m-7*2m-1=0

Wy multiply elements

2m^2+28m^2-4m-14m-1=0

We add all the numbers together, and all the variables

30m^2-18m-1=0

a = 30; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·30·(-1)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{111}}{2*30}=\frac{18-2\sqrt{111}}{60}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{111}}{2*30}=\frac{18+2\sqrt{111}}{60}
$