1/5x+1=9/10x+6

Solution for 1/5x+1=9/10x+6 equation:

1/5x+1=9/10x+6

We move all terms to the left:

1/5x+1-(9/10x+6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/5x-9/10x-6+1=0

We calculate fractions


10x/50x^2+(-45x)/50x^2-6+1=0

We add all the numbers together, and all the variables

10x/50x^2+(-45x)/50x^2-5=0

We multiply all the terms by the denominator


10x+(-45x)-5*50x^2=0

Wy multiply elements

-250x^2+10x+(-45x)=0

We get rid of parentheses

-250x^2+10x-45x=0

We add all the numbers together, and all the variables

-250x^2-35x=0

a = -250; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-250)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-250}=\frac{0}{-500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-250}=\frac{70}{-500}
=-7/50
$