1/2x+1/3x+1/2=14/4

Solution for 1/2x+1/3x+1/2=14/4 equation:

1/2x+1/3x+1/2=14/4

We move all terms to the left:

1/2x+1/3x+1/2-(14/4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+1/3x+1/2-(+14/4)=0

We get rid of parentheses

1/2x+1/3x+1/2-14/4=0

We calculate fractions


(-504x^2)/96x^2+48x/96x^2+32x/96x^2+48x/96x^2=0

We multiply all the terms by the denominator


(-504x^2)+48x+32x+48x=0

We add all the numbers together, and all the variables

(-504x^2)+128x=0

We get rid of parentheses

-504x^2+128x=0

a = -504; b = 128; c = 0;
Δ = b2-4ac
Δ = 1282-4·(-504)·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-128}{2*-504}=\frac{-256}{-1008}
=16/63
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128}{2*-504}=\frac{0}{-1008}
=0
$