(5x-1)/(x+8)=2x-4

Solution for (5x-1)/(x+8)=2x-4 equation:

(5x-1)/(x+8)=2x-4

We move all terms to the left:

(5x-1)/(x+8)-(2x-4)=0


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 get rid of parentheses

(5x-1)/(x+8)-2x+4=0

We multiply all the terms by the denominator


(5x-1)-2x*(x+8)+4*(x+8)=0

We multiply parentheses

-2x^2+(5x-1)-16x+4x+32=0

We get rid of parentheses

-2x^2+5x-16x+4x-1+32=0

We add all the numbers together, and all the variables

-2x^2-7x+31=0

a = -2; b = -7; c = +31;
Δ = b2-4ac
Δ = -72-4·(-2)·31
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{33}}{2*-2}=\frac{7-3\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{33}}{2*-2}=\frac{7+3\sqrt{33}}{-4}
$