((6x-8)(x+4))/x-8=0

Solution for ((6x-8)(x+4))/x-8=0 equation:

((6x-8)(x+4))/x-8=0


Domain of the equation: x!=0

x∈R


We multiply parentheses ..

((+6x^2+24x-8x-32))/x-8=0

We multiply all the terms by the denominator


((+6x^2+24x-8x-32))-8*x=0


We calculate terms in parentheses: +((+6x^2+24x-8x-32)), so:

(+6x^2+24x-8x-32)

We get rid of parentheses

6x^2+24x-8x-32

We add all the numbers together, and all the variables

6x^2+16x-32

Back to the equation:

+(6x^2+16x-32)


We add all the numbers together, and all the variables

-8x+(6x^2+16x-32)=0

We get rid of parentheses

6x^2-8x+16x-32=0

We add all the numbers together, and all the variables

6x^2+8x-32=0

a = 6; b = 8; c = -32;
Δ = b2-4ac
Δ = 82-4·6·(-32)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{13}}{2*6}=\frac{-8-8\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{13}}{2*6}=\frac{-8+8\sqrt{13}}{12}
$