3x-5/x-3=0

Solution for 3x-5/x-3=0 equation:

3x-5/x-3=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x-3*x-5=0

We add all the numbers together, and all the variables

-3x+3x*x-5=0

Wy multiply elements

3x^2-3x-5=0

a = 3; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·3·(-5)
Δ = 69
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{-(-3)-\sqrt{69}}{2*3}=\frac{3-\sqrt{69}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{69}}{2*3}=\frac{3+\sqrt{69}}{6}
$