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

Solution for -(1)/(2)x+3=4-(1)/(4)x equation:

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-4x)/8x^2+2x/8x^2-4+3=0

We add all the numbers together, and all the variables

(-4x)/8x^2+2x/8x^2-1=0

We multiply all the terms by the denominator


(-4x)+2x-1*8x^2=0

We add all the numbers together, and all the variables

2x+(-4x)-1*8x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-8x^2-2x=0

a = -8; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-8)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-8}=\frac{4}{-16}
=-1/4
$