12-1/4x=1/2x+18

Solution for 12-1/4x=1/2x+18 equation:

12-1/4x=1/2x+18

We move all terms to the left:

12-1/4x-(1/2x+18)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+18)!=0

x∈R


We get rid of parentheses

-1/4x-1/2x-18+12=0

We calculate fractions


(-2x)/8x^2+(-4x)/8x^2-18+12=0

We add all the numbers together, and all the variables

(-2x)/8x^2+(-4x)/8x^2-6=0

We multiply all the terms by the denominator


(-2x)+(-4x)-6*8x^2=0

Wy multiply elements

-48x^2+(-2x)+(-4x)=0

We get rid of parentheses

-48x^2-2x-4x=0

We add all the numbers together, and all the variables

-48x^2-6x=0

a = -48; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-48)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-48}=\frac{12}{-96}
=-1/8
$