6-((2/3)(6b-9))=-5b-21

Solution for 6-((2/3)(6b-9))=-5b-21 equation:

6-((2/3)(6b-9))=-5b-21

We move all terms to the left:

6-((2/3)(6b-9))-(-5b-21)=0


Domain of the equation: 3)(6b-9))!=0

b∈R


We add all the numbers together, and all the variables

-((+2/3)(6b-9))-(-5b-21)+6=0

We get rid of parentheses

-((+2/3)(6b-9))+5b+21+6=0

We multiply parentheses ..

-((+12b^2+2/3*-9))+5b+21+6=0

We multiply all the terms by the denominator


-((+12b^2+2+5b*3*-9))+21*3*-9))+6*3*-9))=0


We calculate terms in parentheses: -((+12b^2+2+5b*3*-9)), so:

(+12b^2+2+5b*3*-9)

We get rid of parentheses

12b^2+5b*3*+2-9

We add all the numbers together, and all the variables

12b^2+5b*3*-7

Wy multiply elements

12b^2+15b^2-7

We add all the numbers together, and all the variables

27b^2-7

Back to the equation:

-(27b^2-7)


We add all the numbers together, and all the variables

-(27b^2-7)=0

We get rid of parentheses

-27b^2+7=0

a = -27; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-27)·7
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{21}}{2*-27}=\frac{0-6\sqrt{21}}{-54}
=-\frac{6\sqrt{21}}{-54}
=-\frac{\sqrt{21}}{-9}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{21}}{2*-27}=\frac{0+6\sqrt{21}}{-54}
=\frac{6\sqrt{21}}{-54}
=\frac{\sqrt{21}}{-9}
$