(x+4)*2x/(3x+5)=3

Solution for (x+4)*2x/(3x+5)=3 equation:

(x+4)*2x/(3x+5)=3

We move all terms to the left:

(x+4)*2x/(3x+5)-(3)=0


Domain of the equation: (3x+5)!=0

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

3x!=-5

x!=-5/3

x!=-1+2/3

x∈R


We multiply all the terms by the denominator


(x+4)*2x-3*(3x+5)=0

We multiply parentheses

2x^2+8x-9x-15=0

We add all the numbers together, and all the variables

2x^2-1x-15=0

a = 2; b = -1; c = -15;
Δ = b2-4ac
Δ = -12-4·2·(-15)
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{-(-1)-11}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*2}=\frac{12}{4}
=3
$