3/2x+6=4/5x+9

Solution for 3/2x+6=4/5x+9 equation:

3/2x+6=4/5x+9

We move all terms to the left:

3/2x+6-(4/5x+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-4/5x-9+6=0

We calculate fractions


15x/10x^2+(-8x)/10x^2-9+6=0

We add all the numbers together, and all the variables

15x/10x^2+(-8x)/10x^2-3=0

We multiply all the terms by the denominator


15x+(-8x)-3*10x^2=0

Wy multiply elements

-30x^2+15x+(-8x)=0

We get rid of parentheses

-30x^2+15x-8x=0

We add all the numbers together, and all the variables

-30x^2+7x=0

a = -30; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-30)·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*-30}=\frac{-14}{-60}
=7/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-30}=\frac{0}{-60}
=0
$