2/3+1/5b=5/6;b=

Solution for 2/3+1/5b=5/6;b= equation:

2/3+1/5b=5/6b=

We move all terms to the left:

2/3+1/5b-(5/6b)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 6b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

1/5b-(+5/6b)+2/3=0

We get rid of parentheses

1/5b-5/6b+2/3=0

We calculate fractions


360b^2/270b^2+54b/270b^2+(-225b)/270b^2=0

We multiply all the terms by the denominator


360b^2+54b+(-225b)=0

We get rid of parentheses

360b^2+54b-225b=0

We add all the numbers together, and all the variables

360b^2-171b=0

a = 360; b = -171; c = 0;
Δ = b2-4ac
Δ = -1712-4·360·0
Δ = 29241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29241}=171$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-171)-171}{2*360}=\frac{0}{720}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-171)+171}{2*360}=\frac{342}{720}
=19/40
$