6x+12/x-17=0

Solution for 6x+12/x-17=0 equation:

6x+12/x-17=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


6x*x-17*x+12=0

We add all the numbers together, and all the variables

-17x+6x*x+12=0

Wy multiply elements

6x^2-17x+12=0

a = 6; b = -17; c = +12;
Δ = b2-4ac
Δ = -172-4·6·12
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-1}{2*6}=\frac{16}{12}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+1}{2*6}=\frac{18}{12}
=1+1/2
$