1/4m-6=2m+9

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

1/4m-6=2m+9

We move all terms to the left:

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


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We get rid of parentheses

1/4m-2m-9-6=0

We multiply all the terms by the denominator


-2m*4m-9*4m-6*4m+1=0

Wy multiply elements

-8m^2-36m-24m+1=0

We add all the numbers together, and all the variables

-8m^2-60m+1=0

a = -8; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·(-8)·1
Δ = 3632
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:

$\sqrt{\Delta}=\sqrt{3632}=\sqrt{16*227}=\sqrt{16}*\sqrt{227}=4\sqrt{227}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{227}}{2*-8}=\frac{60-4\sqrt{227}}{-16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{227}}{2*-8}=\frac{60+4\sqrt{227}}{-16}
$