4m+6/m=11

Solution for 4m+6/m=11 equation:

4m+6/m=11

We move all terms to the left:

4m+6/m-(11)=0


Domain of the equation: m!=0

m∈R


We multiply all the terms by the denominator


4m*m-11*m+6=0

We add all the numbers together, and all the variables

-11m+4m*m+6=0

Wy multiply elements

4m^2-11m+6=0

a = 4; b = -11; c = +6;
Δ = b2-4ac
Δ = -112-4·4·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*4}=\frac{6}{8}
=3/4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*4}=\frac{16}{8}
=2
$