3/5x+3/2x+12x/5=180

Solution for 3/5x+3/2x+12x/5=180 equation:

3/5x+3/2x+12x/5=180

We move all terms to the left:

3/5x+3/2x+12x/5-(180)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


24x^2/250x^2+6x/250x^2+375x/250x^2-180=0

We multiply all the terms by the denominator


24x^2+6x+375x-180*250x^2=0

We add all the numbers together, and all the variables

24x^2+381x-180*250x^2=0

Wy multiply elements

24x^2-45000x^2+381x=0

We add all the numbers together, and all the variables

-44976x^2+381x=0

a = -44976; b = 381; c = 0;
Δ = b2-4ac
Δ = 3812-4·(-44976)·0
Δ = 145161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{145161}=381$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(381)-381}{2*-44976}=\frac{-762}{-89952}
=127/14992
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(381)+381}{2*-44976}=\frac{0}{-89952}
=0
$