12/3+3x=4/5x+15

Solution for 12/3+3x=4/5x+15 equation:

12/3+3x=4/5x+15

We move all terms to the left:

12/3+3x-(4/5x+15)=0


Domain of the equation: 5x+15)!=0

x∈R


We add all the numbers together, and all the variables

3x-(4/5x+15)+4=0

We get rid of parentheses

3x-4/5x-15+4=0

We multiply all the terms by the denominator


3x*5x-15*5x+4*5x-4=0

Wy multiply elements

15x^2-75x+20x-4=0

We add all the numbers together, and all the variables

15x^2-55x-4=0

a = 15; b = -55; c = -4;
Δ = b2-4ac
Δ = -552-4·15·(-4)
Δ = 3265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{3265}}{2*15}=\frac{55-\sqrt{3265}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3265}}{2*15}=\frac{55+\sqrt{3265}}{30}
$