3/5x-1/6x-16=13

Solution for 3/5x-1/6x-16=13 equation:

3/5x-1/6x-16=13

We move all terms to the left:

3/5x-1/6x-16-(13)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-1/6x-29=0

We calculate fractions


18x/30x^2+(-5x)/30x^2-29=0

We multiply all the terms by the denominator


18x+(-5x)-29*30x^2=0

Wy multiply elements

-870x^2+18x+(-5x)=0

We get rid of parentheses

-870x^2+18x-5x=0

We add all the numbers together, and all the variables

-870x^2+13x=0

a = -870; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-870)·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*-870}=\frac{-26}{-1740}
=13/870
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-870}=\frac{0}{-1740}
=0
$