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

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

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


Domain of the equation: x!=0

x∈R


We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2+11x+3=0

a = 4; b = 11; c = +3;
Δ = b2-4ac
Δ = 112-4·4·3
Δ = 73
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{-(11)-\sqrt{73}}{2*4}=\frac{-11-\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{73}}{2*4}=\frac{-11+\sqrt{73}}{8}
$