3/5x+6/2x=12

Solution for 3/5x+6/2x=12 equation:

3/5x+6/2x=12

We move all terms to the left:

3/5x+6/2x-(12)=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


6x/10x^2+30x/10x^2-12=0

We multiply all the terms by the denominator


6x+30x-12*10x^2=0

We add all the numbers together, and all the variables

36x-12*10x^2=0

Wy multiply elements

-120x^2+36x=0

a = -120; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-120)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-120}=\frac{-72}{-240}
=3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-120}=\frac{0}{-240}
=0
$