14/6x+8=2+5/2x

Solution for 14/6x+8=2+5/2x equation:

14/6x+8=2+5/2x

We move all terms to the left:

14/6x+8-(2+5/2x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

14/6x-(5/2x+2)+8=0

We get rid of parentheses

14/6x-5/2x-2+8=0

We calculate fractions


28x/12x^2+(-30x)/12x^2-2+8=0

We add all the numbers together, and all the variables

28x/12x^2+(-30x)/12x^2+6=0

We multiply all the terms by the denominator


28x+(-30x)+6*12x^2=0

Wy multiply elements

72x^2+28x+(-30x)=0

We get rid of parentheses

72x^2+28x-30x=0

We add all the numbers together, and all the variables

72x^2-2x=0

a = 72; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·72·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*72}=\frac{4}{144}
=1/36
$