3/2x+4=5/5x+9

Solution for 3/2x+4=5/5x+9 equation:

3/2x+4=5/5x+9

We move all terms to the left:

3/2x+4-(5/5x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+9)!=0

x∈R


We get rid of parentheses

3/2x-5/5x-9+4=0

We calculate fractions


15x/10x^2+(-10x)/10x^2-9+4=0

We add all the numbers together, and all the variables

15x/10x^2+(-10x)/10x^2-5=0

We multiply all the terms by the denominator


15x+(-10x)-5*10x^2=0

Wy multiply elements

-50x^2+15x+(-10x)=0

We get rid of parentheses

-50x^2+15x-10x=0

We add all the numbers together, and all the variables

-50x^2+5x=0

a = -50; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-50)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-50}=\frac{-10}{-100}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-50}=\frac{0}{-100}
=0
$