4/x+1=5/3x+4

Solution for 4/x+1=5/3x+4 equation:

4/x+1=5/3x+4

We move all terms to the left:

4/x+1-(5/3x+4)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

4/x-5/3x-4+1=0

We calculate fractions


12x/3x^2+(-5x)/3x^2-4+1=0

We add all the numbers together, and all the variables

12x/3x^2+(-5x)/3x^2-3=0

We multiply all the terms by the denominator


12x+(-5x)-3*3x^2=0

Wy multiply elements

-9x^2+12x+(-5x)=0

We get rid of parentheses

-9x^2+12x-5x=0

We add all the numbers together, and all the variables

-9x^2+7x=0

a = -9; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-9)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-9}=\frac{-14}{-18}
=7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-9}=\frac{0}{-18}
=0
$