(2x^2-9x+3)/(x-3)=0

Solution for (2x^2-9x+3)/(x-3)=0 equation:

(2x^2-9x+3)/(x-3)=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 multiply all the terms by the denominator


(2x^2-9x+3)=0

We get rid of parentheses

2x^2-9x+3=0

a = 2; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·2·3
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{57}}{2*2}=\frac{9-\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*2}=\frac{9+\sqrt{57}}{4}
$