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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 14x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


14x/28x^2+(-6x)/28x^2-4+2=0

We add all the numbers together, and all the variables

14x/28x^2+(-6x)/28x^2-2=0

We multiply all the terms by the denominator


14x+(-6x)-2*28x^2=0

Wy multiply elements

-56x^2+14x+(-6x)=0

We get rid of parentheses

-56x^2+14x-6x=0

We add all the numbers together, and all the variables

-56x^2+8x=0

a = -56; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-56)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-56}=\frac{-16}{-112}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-56}=\frac{0}{-112}
=0
$