3/2x+9/4x+3/20=12/5

Solution for 3/2x+9/4x+3/20=12/5 equation:

3/2x+9/4x+3/20=12/5

We move all terms to the left:

3/2x+9/4x+3/20-(12/5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x+9/4x+3/20-(+12/5)=0

We get rid of parentheses

3/2x+9/4x+3/20-12/5=0

We calculate fractions


(-7680x^2)/1600x^2+480x^2/1600x^2+2400x/1600x^2+3600x/1600x^2=0

We multiply all the terms by the denominator


(-7680x^2)+480x^2+2400x+3600x=0

We add all the numbers together, and all the variables

480x^2+(-7680x^2)+6000x=0

We get rid of parentheses

480x^2-7680x^2+6000x=0

We add all the numbers together, and all the variables

-7200x^2+6000x=0

a = -7200; b = 6000; c = 0;
Δ = b2-4ac
Δ = 60002-4·(-7200)·0
Δ = 36000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36000000}=6000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6000)-6000}{2*-7200}=\frac{-12000}{-14400}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6000)+6000}{2*-7200}=\frac{0}{-14400}
=0
$