1/4m-14=1/2m-10

Solution for 1/4m-14=1/2m-10 equation:

1/4m-14=1/2m-10

We move all terms to the left:

1/4m-14-(1/2m-10)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 2m-10)!=0

m∈R


We get rid of parentheses

1/4m-1/2m+10-14=0

We calculate fractions


2m/8m^2+(-4m)/8m^2+10-14=0

We add all the numbers together, and all the variables

2m/8m^2+(-4m)/8m^2-4=0

We multiply all the terms by the denominator


2m+(-4m)-4*8m^2=0

Wy multiply elements

-32m^2+2m+(-4m)=0

We get rid of parentheses

-32m^2+2m-4m=0

We add all the numbers together, and all the variables

-32m^2-2m=0

a = -32; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-32)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-32}=\frac{0}{-64}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-32}=\frac{4}{-64}
=-1/16
$