5/(x-6)=3x-2

Solution for 5/(x-6)=3x-2 equation:

5/(x-6)=3x-2

We move all terms to the left:

5/(x-6)-(3x-2)=0


Domain of the equation: (x-6)!=0

We move all terms containing x to the left, all other terms to the right

x!=6

x∈R


We get rid of parentheses

5/(x-6)-3x+2=0

We multiply all the terms by the denominator


-3x*(x-6)+2*(x-6)+5=0

We multiply parentheses

-3x^2+18x+2x-12+5=0

We add all the numbers together, and all the variables

-3x^2+20x-7=0

a = -3; b = 20; c = -7;
Δ = b2-4ac
Δ = 202-4·(-3)·(-7)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{79}}{2*-3}=\frac{-20-2\sqrt{79}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{79}}{2*-3}=\frac{-20+2\sqrt{79}}{-6}
$