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

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

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


Domain of the equation: (4x+3)!=0

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

4x!=-3

x!=-3/4

x!=-3/4

x∈R


We multiply all the terms by the denominator


(x^2+2x)=0

We get rid of parentheses

x^2+2x=0

a = 1; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·1·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*1}=\frac{0}{2}
=0
$