(2x+1)(x-3)/x-4=0

Solution for (2x+1)(x-3)/x-4=0 equation:

(2x+1)(x-3)/x-4=0


Domain of the equation: x!=0

x∈R


We multiply parentheses ..

(+2x^2-6x+x-3)/x-4=0

We multiply all the terms by the denominator


(+2x^2-6x+x-3)-4*x=0

We add all the numbers together, and all the variables

(+2x^2-6x+x-3)-4x=0

We get rid of parentheses

2x^2-6x+x-4x-3=0

We add all the numbers together, and all the variables

2x^2-9x-3=0

a = 2; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·2·(-3)
Δ = 105
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{105}}{2*2}=\frac{9-\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*2}=\frac{9+\sqrt{105}}{4}
$