5/x-3-5/6x-18=-8

Solution for 5/x-3-5/6x-18=-8 equation:

5/x-3-5/6x-18=-8

We move all terms to the left:

5/x-3-5/6x-18-(-8)=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-5/6x-13=0

We calculate fractions


30x/6x^2+(-5x)/6x^2-13=0

We multiply all the terms by the denominator


30x+(-5x)-13*6x^2=0

Wy multiply elements

-78x^2+30x+(-5x)=0

We get rid of parentheses

-78x^2+30x-5x=0

We add all the numbers together, and all the variables

-78x^2+25x=0

a = -78; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-78)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-78}=\frac{-50}{-156}
=25/78
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-78}=\frac{0}{-156}
=0
$