12+1/4x-15=18-1/2x

Solution for 12+1/4x-15=18-1/2x equation:

12+1/4x-15=18-1/2x

We move all terms to the left:

12+1/4x-15-(18-1/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(-1/2x+18)+12-15=0

We add all the numbers together, and all the variables

1/4x-(-1/2x+18)-3=0

We get rid of parentheses

1/4x+1/2x-18-3=0

We calculate fractions


2x/8x^2+4x/8x^2-18-3=0

We add all the numbers together, and all the variables

2x/8x^2+4x/8x^2-21=0

We multiply all the terms by the denominator


2x+4x-21*8x^2=0

We add all the numbers together, and all the variables

6x-21*8x^2=0

Wy multiply elements

-168x^2+6x=0

a = -168; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-168)·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*-168}=\frac{-12}{-336}
=1/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-168}=\frac{0}{-336}
=0
$