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

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

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


Domain of the equation: (x+1)!=0

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

x!=-1

x∈R


We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We get rid of parentheses

4x^2-12x-1x+3=0

We add all the numbers together, and all the variables

4x^2-13x+3=0

a = 4; b = -13; c = +3;
Δ = b2-4ac
Δ = -132-4·4·3
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-11}{2*4}=\frac{2}{8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+11}{2*4}=\frac{24}{8}
=3
$