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

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

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

We move all terms to the left:

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


Domain of the equation: 10b!=0

b!=0/10

b!=0

b∈R



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

b∈R


We get rid of parentheses

9/10b-19/20b-1-4=0

We calculate fractions


180b/200b^2+(-190b)/200b^2-1-4=0

We add all the numbers together, and all the variables

180b/200b^2+(-190b)/200b^2-5=0

We multiply all the terms by the denominator


180b+(-190b)-5*200b^2=0

Wy multiply elements

-1000b^2+180b+(-190b)=0

We get rid of parentheses

-1000b^2+180b-190b=0

We add all the numbers together, and all the variables

-1000b^2-10b=0

a = -1000; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-1000)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-1000}=\frac{0}{-2000}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-1000}=\frac{20}{-2000}
=-1/100
$