5/x+3-2/6x+18=11

Solution for 5/x+3-2/6x+18=11 equation:

5/x+3-2/6x+18=11

We move all terms to the left:

5/x+3-2/6x+18-(11)=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

5/x-2/6x+10=0

We calculate fractions


30x/6x^2+(-2x)/6x^2+10=0

We multiply all the terms by the denominator


30x+(-2x)+10*6x^2=0

Wy multiply elements

60x^2+30x+(-2x)=0

We get rid of parentheses

60x^2+30x-2x=0

We add all the numbers together, and all the variables

60x^2+28x=0

a = 60; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·60·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*60}=\frac{-56}{120}
=-7/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*60}=\frac{0}{120}
=0
$