(28/m+7)+21=3m

Solution for (28/m+7)+21=3m equation:

(28/m+7)+21=3m

We move all terms to the left:

(28/m+7)+21-(3m)=0


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

m∈R


We add all the numbers together, and all the variables

-3m+(28/m+7)+21=0

We get rid of parentheses

-3m+28/m+7+21=0

We multiply all the terms by the denominator


-3m*m+7*m+21*m+28=0

We add all the numbers together, and all the variables

28m-3m*m+28=0

Wy multiply elements

-3m^2+28m+28=0

a = -3; b = 28; c = +28;
Δ = b2-4ac
Δ = 282-4·(-3)·28
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{70}}{2*-3}=\frac{-28-4\sqrt{70}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{70}}{2*-3}=\frac{-28+4\sqrt{70}}{-6}
$