6+4/5b=9/19b

Solution for 6+4/5b=9/19b equation:

6+4/5b=9/19b

We move all terms to the left:

6+4/5b-(9/19b)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 19b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

4/5b-(+9/19b)+6=0

We get rid of parentheses

4/5b-9/19b+6=0

We calculate fractions


76b/95b^2+(-45b)/95b^2+6=0

We multiply all the terms by the denominator


76b+(-45b)+6*95b^2=0

Wy multiply elements

570b^2+76b+(-45b)=0

We get rid of parentheses

570b^2+76b-45b=0

We add all the numbers together, and all the variables

570b^2+31b=0

a = 570; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·570·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*570}=\frac{-62}{1140}
=-31/570
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*570}=\frac{0}{1140}
=0
$