1/5x-5=1/6x+10

Solution for 1/5x-5=1/6x+10 equation:

1/5x-5=1/6x+10

We move all terms to the left:

1/5x-5-(1/6x+10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x+10)!=0

x∈R


We get rid of parentheses

1/5x-1/6x-10-5=0

We calculate fractions


6x/30x^2+(-5x)/30x^2-10-5=0

We add all the numbers together, and all the variables

6x/30x^2+(-5x)/30x^2-15=0

We multiply all the terms by the denominator


6x+(-5x)-15*30x^2=0

Wy multiply elements

-450x^2+6x+(-5x)=0

We get rid of parentheses

-450x^2+6x-5x=0

We add all the numbers together, and all the variables

-450x^2+x=0

a = -450; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-450)·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*-450}=\frac{-2}{-900}
=1/450
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-450}=\frac{0}{-900}
=0
$