5/4x+7=3/x+3

Solution for 5/4x+7=3/x+3 equation:

5/4x+7=3/x+3

We move all terms to the left:

5/4x+7-(3/x+3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

5/4x-3/x-3+7=0

We calculate fractions


5x/4x^2+(-12x)/4x^2-3+7=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


5x+(-12x)+4*4x^2=0

Wy multiply elements

16x^2+5x+(-12x)=0

We get rid of parentheses

16x^2+5x-12x=0

We add all the numbers together, and all the variables

16x^2-7x=0

a = 16; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·16·0
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*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*16}=\frac{14}{32}
=7/16
$