1/2x+5=6+1/4x

Solution for 1/2x+5=6+1/4x equation:

1/2x+5=6+1/4x

We move all terms to the left:

1/2x+5-(6+1/4x)=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+6)+5=0

We get rid of parentheses

1/2x-1/4x-6+5=0

We calculate fractions


4x/8x^2+(-2x)/8x^2-6+5=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

Wy multiply elements

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

We get rid of parentheses

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