1/2b-9=10+4/5b

Solution for 1/2b-9=10+4/5b equation:

1/2b-9=10+4/5b

We move all terms to the left:

1/2b-9-(10+4/5b)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 5b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

1/2b-(4/5b+10)-9=0

We get rid of parentheses

1/2b-4/5b-10-9=0

We calculate fractions


5b/10b^2+(-8b)/10b^2-10-9=0

We add all the numbers together, and all the variables

5b/10b^2+(-8b)/10b^2-19=0

We multiply all the terms by the denominator


5b+(-8b)-19*10b^2=0

Wy multiply elements

-190b^2+5b+(-8b)=0

We get rid of parentheses

-190b^2+5b-8b=0

We add all the numbers together, and all the variables

-190b^2-3b=0

a = -190; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-190)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-190}=\frac{0}{-380}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-190}=\frac{6}{-380}
=-3/190
$