b(b+32)=6(8+5b)

Solution for b(b+32)=6(8+5b) equation:

b(b+32)=6(8+5b)

We move all terms to the left:

b(b+32)-(6(8+5b))=0

We add all the numbers together, and all the variables

b(b+32)-(6(5b+8))=0

We multiply parentheses

b^2+32b-(6(5b+8))=0


We calculate terms in parentheses: -(6(5b+8)), so:

6(5b+8)

We multiply parentheses

30b+48

Back to the equation:

-(30b+48)


We get rid of parentheses

b^2+32b-30b-48=0

We add all the numbers together, and all the variables

b^2+2b-48=0

a = 1; b = 2; c = -48;
Δ = b2-4ac
Δ = 22-4·1·(-48)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*1}=\frac{-16}{2}
=-8
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*1}=\frac{12}{2}
=6
$