1/3x+2/5x=77

Solution for 1/3x+2/5x=77 equation:

1/3x+2/5x=77

We move all terms to the left:

1/3x+2/5x-(77)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


5x/15x^2+6x/15x^2-77=0

We multiply all the terms by the denominator


5x+6x-77*15x^2=0

We add all the numbers together, and all the variables

11x-77*15x^2=0

Wy multiply elements

-1155x^2+11x=0

a = -1155; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-1155)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-1155}=\frac{-22}{-2310}
=1/105
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-1155}=\frac{0}{-2310}
=0
$