6/m+2+14=7m

Solution for 6/m+2+14=7m equation:

6/m+2+14=7m

We move all terms to the left:

6/m+2+14-(7m)=0


Domain of the equation: m!=0

m∈R


We add all the numbers together, and all the variables

-7m+6/m+16=0

We multiply all the terms by the denominator


-7m*m+16*m+6=0

We add all the numbers together, and all the variables

16m-7m*m+6=0

Wy multiply elements

-7m^2+16m+6=0

a = -7; b = 16; c = +6;
Δ = b2-4ac
Δ = 162-4·(-7)·6
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{106}}{2*-7}=\frac{-16-2\sqrt{106}}{-14}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{106}}{2*-7}=\frac{-16+2\sqrt{106}}{-14}
$