14/m+3m=22

Solution for 14/m+3m=22 equation:

14/m+3m=22

We move all terms to the left:

14/m+3m-(22)=0


Domain of the equation: m!=0

m∈R


We add all the numbers together, and all the variables

3m+14/m-22=0

We multiply all the terms by the denominator


3m*m-22*m+14=0

We add all the numbers together, and all the variables

-22m+3m*m+14=0

Wy multiply elements

3m^2-22m+14=0

a = 3; b = -22; c = +14;
Δ = b2-4ac
Δ = -222-4·3·14
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{79}}{2*3}=\frac{22-2\sqrt{79}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{79}}{2*3}=\frac{22+2\sqrt{79}}{6}
$