16+4x-(-2x)/x+1+3=-1

Solution for 16+4x-(-2x)/x+1+3=-1 equation:

16+4x-(-2x)/x+1+3=-1

We move all terms to the left:

16+4x-(-2x)/x+1+3-(-1)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x-(-2x)/x+21=0

We multiply all the terms by the denominator


4x*x-(-2x)+21*x=0

We add all the numbers together, and all the variables

21x+4x*x-(-2x)=0

Wy multiply elements

4x^2+21x-(-2x)=0

We get rid of parentheses

4x^2+21x+2x=0

We add all the numbers together, and all the variables

4x^2+23x=0

a = 4; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·4·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*4}=\frac{-46}{8}
=-5+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*4}=\frac{0}{8}
=0
$