5/m+6=14m=

Solution for 5/m+6=14m= equation:

5/m+6=14m=

We move all terms to the left:

5/m+6-(14m)=0


Domain of the equation: m!=0

m∈R


We add all the numbers together, and all the variables

-14m+5/m+6=0

We multiply all the terms by the denominator


-14m*m+6*m+5=0

We add all the numbers together, and all the variables

6m-14m*m+5=0

Wy multiply elements

-14m^2+6m+5=0

a = -14; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-14)·5
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{-(6)-2\sqrt{79}}{2*-14}=\frac{-6-2\sqrt{79}}{-28}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{79}}{2*-14}=\frac{-6+2\sqrt{79}}{-28}
$