1/4m-6=2m+18

Solution for 1/4m-6=2m+18 equation:

1/4m-6=2m+18

We move all terms to the left:

1/4m-6-(2m+18)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We get rid of parentheses

1/4m-2m-18-6=0

We multiply all the terms by the denominator


-2m*4m-18*4m-6*4m+1=0

Wy multiply elements

-8m^2-72m-24m+1=0

We add all the numbers together, and all the variables

-8m^2-96m+1=0

a = -8; b = -96; c = +1;
Δ = b2-4ac
Δ = -962-4·(-8)·1
Δ = 9248
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:

$\sqrt{\Delta}=\sqrt{9248}=\sqrt{4624*2}=\sqrt{4624}*\sqrt{2}=68\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-68\sqrt{2}}{2*-8}=\frac{96-68\sqrt{2}}{-16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+68\sqrt{2}}{2*-8}=\frac{96+68\sqrt{2}}{-16}
$