(2)/(x)+(-3)/(x+8)=4

Solution for (2)/(x)+(-3)/(x+8)=4 equation:

(2)/(x)+(-3)/(x+8)=4

We move all terms to the left:

(2)/(x)+(-3)/(x+8)-(4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: (x+8)!=0

We move all terms containing x to the left, all other terms to the right

x!=-8

x∈R


We calculate fractions


(2x+16)/(x^2+8x)+(-3x)/(x^2+8x)-4=0

We multiply all the terms by the denominator


(2x+16)+(-3x)-4*(x^2+8x)=0

We multiply parentheses

-4x^2+(2x+16)+(-3x)-32x=0

We get rid of parentheses

-4x^2+2x-3x-32x+16=0

We add all the numbers together, and all the variables

-4x^2-33x+16=0

a = -4; b = -33; c = +16;
Δ = b2-4ac
Δ = -332-4·(-4)·16
Δ = 1345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-\sqrt{1345}}{2*-4}=\frac{33-\sqrt{1345}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1345}}{2*-4}=\frac{33+\sqrt{1345}}{-8}
$