(3x^2-16x+21)/(x-3)=x

Solution for (3x^2-16x+21)/(x-3)=x equation:

(3x^2-16x+21)/(x-3)=x

We move all terms to the left:

(3x^2-16x+21)/(x-3)-(x)=0


Domain of the equation: (x-3)!=0

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

x!=3

x∈R


We add all the numbers together, and all the variables

-1x+(3x^2-16x+21)/(x-3)=0

We multiply all the terms by the denominator


-1x*(x-3)+(3x^2-16x+21)=0

We multiply parentheses

-x^2+3x+(3x^2-16x+21)=0

We get rid of parentheses

-x^2+3x^2+3x-16x+21=0

We add all the numbers together, and all the variables

2x^2-13x+21=0

a = 2; b = -13; c = +21;
Δ = b2-4ac
Δ = -132-4·2·21
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{-(-13)-1}{2*2}=\frac{12}{4}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+1}{2*2}=\frac{14}{4}
=3+1/2
$