/9m-27+3m=7m+43

Solution for /9m-27+3m=7m+43 equation:

/9m-27+3m=7m+43

We move all terms to the left:

/9m-27+3m-(7m+43)=0


Domain of the equation: 9m!=0

m!=0/9

m!=0

m∈R


We add all the numbers together, and all the variables

3m+/9m-(7m+43)-27=0

We get rid of parentheses

3m+/9m-7m-43-27=0

We multiply all the terms by the denominator


3m*9m-7m*9m-43*9m-27*9m+=0

We add all the numbers together, and all the variables

3m*9m-7m*9m-43*9m-27*9m=0

Wy multiply elements

27m^2-63m^2-387m-243m=0

We add all the numbers together, and all the variables

-36m^2-630m=0

a = -36; b = -630; c = 0;
Δ = b2-4ac
Δ = -6302-4·(-36)·0
Δ = 396900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{396900}=630$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-630}{2*-36}=\frac{0}{-72}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+630}{2*-36}=\frac{1260}{-72}
=-17+1/2
$