1/2x+3/4=1/4x+6

Solution for 1/2x+3/4=1/4x+6 equation:

1/2x+3/4=1/4x+6

We move all terms to the left:

1/2x+3/4-(1/4x+6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+6)!=0

x∈R


We get rid of parentheses

1/2x-1/4x-6+3/4=0

We calculate fractions


64x/128x^2+(-2x)/128x^2+6x/128x^2-6=0

We multiply all the terms by the denominator


64x+(-2x)+6x-6*128x^2=0

We add all the numbers together, and all the variables

70x+(-2x)-6*128x^2=0

Wy multiply elements

-768x^2+70x+(-2x)=0

We get rid of parentheses

-768x^2+70x-2x=0

We add all the numbers together, and all the variables

-768x^2+68x=0

a = -768; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·(-768)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*-768}=\frac{-136}{-1536}
=17/192
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*-768}=\frac{0}{-1536}
=0
$