21/3x+1/5x=76

Solution for 21/3x+1/5x=76 equation:

21/3x+1/5x=76

We move all terms to the left:

21/3x+1/5x-(76)=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


105x/15x^2+3x/15x^2-76=0

We multiply all the terms by the denominator


105x+3x-76*15x^2=0

We add all the numbers together, and all the variables

108x-76*15x^2=0

Wy multiply elements

-1140x^2+108x=0

a = -1140; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·(-1140)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*-1140}=\frac{-216}{-2280}
=9/95
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*-1140}=\frac{0}{-2280}
=0
$