2/3x+4+1/5x=43

Solution for 2/3x+4+1/5x=43 equation:

2/3x+4+1/5x=43

We move all terms to the left:

2/3x+4+1/5x-(43)=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 add all the numbers together, and all the variables

2/3x+1/5x-39=0

We calculate fractions


10x/15x^2+3x/15x^2-39=0

We multiply all the terms by the denominator


10x+3x-39*15x^2=0

We add all the numbers together, and all the variables

13x-39*15x^2=0

Wy multiply elements

-585x^2+13x=0

a = -585; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-585)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-585}=\frac{-26}{-1170}
=1/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-585}=\frac{0}{-1170}
=0
$