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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


64x/128x^2+(-6x)/128x^2+2x/128x^2-4=0

We multiply all the terms by the denominator


64x+(-6x)+2x-4*128x^2=0

We add all the numbers together, and all the variables

66x+(-6x)-4*128x^2=0

Wy multiply elements

-512x^2+66x+(-6x)=0

We get rid of parentheses

-512x^2+66x-6x=0

We add all the numbers together, and all the variables

-512x^2+60x=0

a = -512; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-512)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-512}=\frac{-120}{-1024}
=15/128
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-512}=\frac{0}{-1024}
=0
$