1/5x+10+3x/x+2=0

Solution for 1/5x+10+3x/x+2=0 equation:

1/5x+10+3x/x+2=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1/5x+3x/x+12=0

We calculate fractions


15x^2/5x^2+x/5x^2+12=0

We multiply all the terms by the denominator


15x^2+x+12*5x^2=0

Wy multiply elements

15x^2+60x^2+x=0

We add all the numbers together, and all the variables

75x^2+x=0

a = 75; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·75·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*75}=\frac{-2}{150}
=-1/75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*75}=\frac{0}{150}
=0
$