1+2/x-80/6x=3

Solution for 1+2/x-80/6x=3 equation:

1+2/x-80/6x=3

We move all terms to the left:

1+2/x-80/6x-(3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

2/x-80/6x-2=0

We calculate fractions


12x/6x^2+(-80x)/6x^2-2=0

We multiply all the terms by the denominator


12x+(-80x)-2*6x^2=0

Wy multiply elements

-12x^2+12x+(-80x)=0

We get rid of parentheses

-12x^2+12x-80x=0

We add all the numbers together, and all the variables

-12x^2-68x=0

a = -12; b = -68; c = 0;
Δ = b2-4ac
Δ = -682-4·(-12)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-68}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+68}{2*-12}=\frac{136}{-24}
=-5+2/3
$