12/5x+3/2x=29

Solution for 12/5x+3/2x=29 equation:

12/5x+3/2x=29

We move all terms to the left:

12/5x+3/2x-(29)=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/10x^2+15x/10x^2-29=0

We multiply all the terms by the denominator


24x+15x-29*10x^2=0

We add all the numbers together, and all the variables

39x-29*10x^2=0

Wy multiply elements

-290x^2+39x=0

a = -290; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-290)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*-290}=\frac{-78}{-580}
=39/290
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-290}=\frac{0}{-580}
=0
$