4/5b+6=9/10b

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



4/5b+6=9/10b
We move all terms to the left:
4/5b+6-(9/10b)=0
Domain of the equation: 5b!=0
b!=0/5
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)+6=0
We get rid of parentheses
4/5b-9/10b+6=0
We calculate fractions
40b/50b^2+(-45b)/50b^2+6=0
We multiply all the terms by the denominator
40b+(-45b)+6*50b^2=0
Wy multiply elements
300b^2+40b+(-45b)=0
We get rid of parentheses
300b^2+40b-45b=0
We add all the numbers together, and all the variables
300b^2-5b=0
a = 300; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·300·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*300}=\frac{0}{600} =0 $
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*300}=\frac{10}{600} =1/60 $

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