4m-6.5/m=2

Solution for 4m-6.5/m=2 equation:

4m-6.5/m=2

We move all terms to the left:

4m-6.5/m-(2)=0


Domain of the equation: m!=0

m∈R


We multiply all the terms by the denominator


4m*m-2*m-6.5=0

We add all the numbers together, and all the variables

-2m+4m*m-6.5=0

Wy multiply elements

4m^2-2m-6.5=0

a = 4; b = -2; c = -6.5;
Δ = b2-4ac
Δ = -22-4·4·(-6.5)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{3}}{2*4}=\frac{2-6\sqrt{3}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{3}}{2*4}=\frac{2+6\sqrt{3}}{8}
$