9/10b-3=-19/20b+2

Solution for 9/10b-3=-19/20b+2 equation:

9/10b-3=-19/20b+2

We move all terms to the left:

9/10b-3-(-19/20b+2)=0


Domain of the equation: 10b!=0

b!=0/10

b!=0

b∈R



Domain of the equation: 20b+2)!=0

b∈R


We get rid of parentheses

9/10b+19/20b-2-3=0

We calculate fractions


180b/200b^2+190b/200b^2-2-3=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

We add all the numbers together, and all the variables

370b-5*200b^2=0

Wy multiply elements

-1000b^2+370b=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:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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