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

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

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

We move all terms to the left:

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


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

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

x!=-3

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(5x^2+20x)/(5x^2+15x)+(2x+6)/(5x^2+15x)=0

We multiply all the terms by the denominator


(5x^2+20x)+(2x+6)=0

We get rid of parentheses

5x^2+20x+2x+6=0

We add all the numbers together, and all the variables

5x^2+22x+6=0

a = 5; b = 22; c = +6;
Δ = b2-4ac
Δ = 222-4·5·6
Δ = 364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{91}}{2*5}=\frac{-22-2\sqrt{91}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{91}}{2*5}=\frac{-22+2\sqrt{91}}{10}
$