1/2x+6=5/4x

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

1/2x+6=5/4x

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


4x/8x^2+(-10x)/8x^2+6=0

We multiply all the terms by the denominator


4x+(-10x)+6*8x^2=0

Wy multiply elements

48x^2+4x+(-10x)=0

We get rid of parentheses

48x^2+4x-10x=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
$