6x-4/x+5=0

Solution for 6x-4/x+5=0 equation:

6x-4/x+5=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


6x*x+5*x-4=0

We add all the numbers together, and all the variables

5x+6x*x-4=0

Wy multiply elements

6x^2+5x-4=0

a = 6; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·6·(-4)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*6}=\frac{-16}{12}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*6}=\frac{6}{12}
=1/2
$