3x-4/x+8=0

Solution for 3x-4/x+8=0 equation:

3x-4/x+8=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x+8*x-4=0

We add all the numbers together, and all the variables

8x+3x*x-4=0

Wy multiply elements

3x^2+8x-4=0

a = 3; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·3·(-4)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*3}=\frac{-8-4\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*3}=\frac{-8+4\sqrt{7}}{6}
$