(1/4)m-6=2(m+9)

Solution for (1/4)m-6=2(m+9) equation:

(1/4)m-6=2(m+9)

We move all terms to the left:

(1/4)m-6-(2(m+9))=0


Domain of the equation: 4)m!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

(+1/4)m-(2(m+9))-6=0

We multiply parentheses

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


We calculate terms in parentheses: -(2(m+9)), so:

2(m+9)

We multiply parentheses

2m+18

Back to the equation:

-(2m+18)


We get rid of parentheses

m^2-2m-18-6=0

We add all the numbers together, and all the variables

m^2-2m-24=0

a = 1; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·1·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*1}=\frac{-8}{2}
=-4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*1}=\frac{12}{2}
=6
$