-5/6b-10=-3+2/3b

Solution for -5/6b-10=-3+2/3b equation:

-5/6b-10=-3+2/3b

We move all terms to the left:

-5/6b-10-(-3+2/3b)=0


Domain of the equation: 6b!=0

b!=0/6

b!=0

b∈R



Domain of the equation: 3b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-5/6b-(2/3b-3)-10=0

We get rid of parentheses

-5/6b-2/3b+3-10=0

We calculate fractions


(-15b)/18b^2+(-12b)/18b^2+3-10=0

We add all the numbers together, and all the variables

(-15b)/18b^2+(-12b)/18b^2-7=0

We multiply all the terms by the denominator


(-15b)+(-12b)-7*18b^2=0

Wy multiply elements

-126b^2+(-15b)+(-12b)=0

We get rid of parentheses

-126b^2-15b-12b=0

We add all the numbers together, and all the variables

-126b^2-27b=0

a = -126; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-126)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-126}=\frac{0}{-252}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-126}=\frac{54}{-252}
=-3/14
$