9/10x-4=-19/20x+1

Solution for 9/10x-4=-19/20x+1 equation:

9/10x-4=-19/20x+1

We move all terms to the left:

9/10x-4-(-19/20x+1)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 20x+1)!=0

x∈R


We get rid of parentheses

9/10x+19/20x-1-4=0

We calculate fractions


180x/200x^2+190x/200x^2-1-4=0

We add all the numbers together, and all the variables

180x/200x^2+190x/200x^2-5=0

We multiply all the terms by the denominator


180x+190x-5*200x^2=0

We add all the numbers together, and all the variables

370x-5*200x^2=0

Wy multiply elements

-1000x^2+370x=0

a = -1000; b = 370; c = 0;
Δ = b2-4ac
Δ = 3702-4·(-1000)·0
Δ = 136900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{136900}=370$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(370)-370}{2*-1000}=\frac{-740}{-2000}
=37/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(370)+370}{2*-1000}=\frac{0}{-2000}
=0
$