12/5x+3/4x=29

Solution for 12/5x+3/4x=29 equation:

12/5x+3/4x=29

We move all terms to the left:

12/5x+3/4x-(29)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


48x/20x^2+15x/20x^2-29=0

We multiply all the terms by the denominator


48x+15x-29*20x^2=0

We add all the numbers together, and all the variables

63x-29*20x^2=0

Wy multiply elements

-580x^2+63x=0

a = -580; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-580)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-580}=\frac{-126}{-1160}
=63/580
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-580}=\frac{0}{-1160}
=0
$