9(m+2)=-6(m+7)m=

Solution for 9(m+2)=-6(m+7)m= equation:

9(m+2)=-6(m+7)m=

We move all terms to the left:

9(m+2)-(-6(m+7)m)=0

We multiply parentheses

9m-(-6(m+7)m)+18=0


We calculate terms in parentheses: -(-6(m+7)m), so:

-6(m+7)m

We multiply parentheses

-6m^2-42m

Back to the equation:

-(-6m^2-42m)


We get rid of parentheses

6m^2+42m+9m+18=0

We add all the numbers together, and all the variables

6m^2+51m+18=0

a = 6; b = 51; c = +18;
Δ = b2-4ac
Δ = 512-4·6·18
Δ = 2169
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:

$\sqrt{\Delta}=\sqrt{2169}=\sqrt{9*241}=\sqrt{9}*\sqrt{241}=3\sqrt{241}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-3\sqrt{241}}{2*6}=\frac{-51-3\sqrt{241}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+3\sqrt{241}}{2*6}=\frac{-51+3\sqrt{241}}{12}
$