5x-8/x+6=0

Solution for 5x-8/x+6=0 equation:

5x-8/x+6=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x*x+6*x-8=0

We add all the numbers together, and all the variables

6x+5x*x-8=0

Wy multiply elements

5x^2+6x-8=0

a = 5; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·5·(-8)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*5}=\frac{8}{10}
=4/5
$