1/2m+3=m-4

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

1/2m+3=m-4

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -2; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·(-2)·1
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{51}}{2*-2}=\frac{-14-2\sqrt{51}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{51}}{2*-2}=\frac{-14+2\sqrt{51}}{-4}
$