(1/3)(6m+21)=m-7

Solution for (1/3)(6m+21)=m-7 equation:

(1/3)(6m+21)=m-7

We move all terms to the left:

(1/3)(6m+21)-(m-7)=0


Domain of the equation: 3)(6m+21)!=0

m∈R


We add all the numbers together, and all the variables

(+1/3)(6m+21)-(m-7)=0

We get rid of parentheses

(+1/3)(6m+21)-m+7=0

We multiply parentheses ..

(+6m^2+1/3*21)-m+7=0

We multiply all the terms by the denominator


(+6m^2+1-m*3*21)+7*3*21)=0

We add all the numbers together, and all the variables

(+6m^2+1-m*3*21)=0

We get rid of parentheses

6m^2-m*3*21+1=0

Wy multiply elements

6m^2-63m*2+1=0

Wy multiply elements

6m^2-126m+1=0

a = 6; b = -126; c = +1;
Δ = b2-4ac
Δ = -1262-4·6·1
Δ = 15852
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:

$\sqrt{\Delta}=\sqrt{15852}=\sqrt{4*3963}=\sqrt{4}*\sqrt{3963}=2\sqrt{3963}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3963}}{2*6}=\frac{126-2\sqrt{3963}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3963}}{2*6}=\frac{126+2\sqrt{3963}}{12}
$