6+4/5b+9/10b=8+2/10b

Solution for 6+4/5b+9/10b=8+2/10b equation:

6+4/5b+9/10b=8+2/10b

We move all terms to the left:

6+4/5b+9/10b-(8+2/10b)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 10b!=0

b!=0/10

b!=0

b∈R



Domain of the equation: 10b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

4/5b+9/10b-(2/10b+8)+6=0

We get rid of parentheses

4/5b+9/10b-2/10b-8+6=0

We calculate fractions


40b/50b^2+(-10b+9)/50b^2-8+6=0

We add all the numbers together, and all the variables

40b/50b^2+(-10b+9)/50b^2-2=0

We multiply all the terms by the denominator


40b+(-10b+9)-2*50b^2=0

Wy multiply elements

-100b^2+40b+(-10b+9)=0

We get rid of parentheses

-100b^2+40b-10b+9=0

We add all the numbers together, and all the variables

-100b^2+30b+9=0

a = -100; b = 30; c = +9;
Δ = b2-4ac
Δ = 302-4·(-100)·9
Δ = 4500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30\sqrt{5}}{2*-100}=\frac{-30-30\sqrt{5}}{-200}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30\sqrt{5}}{2*-100}=\frac{-30+30\sqrt{5}}{-200}
$