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

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

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


Domain of the equation: x!=0

x∈R


We multiply parentheses ..

((+4x^2-12x-1x+3))/x+3=0

We multiply all the terms by the denominator


((+4x^2-12x-1x+3))+3*x=0


We calculate terms in parentheses: +((+4x^2-12x-1x+3)), so:

(+4x^2-12x-1x+3)

We get rid of parentheses

4x^2-12x-1x+3

We add all the numbers together, and all the variables

4x^2-13x+3

Back to the equation:

+(4x^2-13x+3)


We add all the numbers together, and all the variables

3x+(4x^2-13x+3)=0

We get rid of parentheses

4x^2+3x-13x+3=0

We add all the numbers together, and all the variables

4x^2-10x+3=0

a = 4; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·4·3
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{13}}{2*4}=\frac{10-2\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{13}}{2*4}=\frac{10+2\sqrt{13}}{8}
$