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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


18x^2/96x^2+48x/96x^2+(-32x)/96x^2-1=0

We multiply all the terms by the denominator


18x^2+48x+(-32x)-1*96x^2=0

Wy multiply elements

18x^2-96x^2+48x+(-32x)=0

We get rid of parentheses

18x^2-96x^2+48x-32x=0

We add all the numbers together, and all the variables

-78x^2+16x=0

a = -78; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-78)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-78}=\frac{-32}{-156}
=8/39
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-78}=\frac{0}{-156}
=0
$