21/(m+7)+14=2m

Solution for 21/(m+7)+14=2m equation:

21/(m+7)+14=2m

We move all terms to the left:

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


Domain of the equation: (m+7)!=0

We move all terms containing m to the left, all other terms to the right

m!=-7

m∈R


We add all the numbers together, and all the variables

-2m+21/(m+7)+14=0

We multiply all the terms by the denominator


-2m*(m+7)+14*(m+7)+21=0

We multiply parentheses

-2m^2-14m+14m+98+21=0

We add all the numbers together, and all the variables

-2m^2+119=0

a = -2; b = 0; c = +119;
Δ = b2-4ac
Δ = 02-4·(-2)·119
Δ = 952
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:

$\sqrt{\Delta}=\sqrt{952}=\sqrt{4*238}=\sqrt{4}*\sqrt{238}=2\sqrt{238}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{238}}{2*-2}=\frac{0-2\sqrt{238}}{-4}
=-\frac{2\sqrt{238}}{-4}
=-\frac{\sqrt{238}}{-2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{238}}{2*-2}=\frac{0+2\sqrt{238}}{-4}
=\frac{2\sqrt{238}}{-4}
=\frac{\sqrt{238}}{-2}
$