4/x+3-8/6x+18=-4

Solution for 4/x+3-8/6x+18=-4 equation:

4/x+3-8/6x+18=-4

We move all terms to the left:

4/x+3-8/6x+18-(-4)=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

4/x-8/6x+25=0

We calculate fractions


24x/6x^2+(-8x)/6x^2+25=0

We multiply all the terms by the denominator


24x+(-8x)+25*6x^2=0

Wy multiply elements

150x^2+24x+(-8x)=0

We get rid of parentheses

150x^2+24x-8x=0

We add all the numbers together, and all the variables

150x^2+16x=0

a = 150; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·150·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*150}=\frac{-32}{300}
=-8/75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*150}=\frac{0}{300}
=0
$