42=(1/2)*(b)*(b+3)

Solution for 42=(1/2)*(b)*(b+3) equation:

42=(1/2)(b)(b+3)

We move all terms to the left:

42-((1/2)(b)(b+3))=0


Domain of the equation: 2)b(b+3))!=0

b∈R


We add all the numbers together, and all the variables

-((+1/2)b(b+3))+42=0

We multiply all the terms by the denominator


-((+1+42*2)b(b+3))=0


We calculate terms in parentheses: -((+1+42*2)b(b+3)), so:

(+1+42*2)b(b+3)

We add all the numbers together, and all the variables

85b(b+3)

We multiply parentheses

85b^2+255b

Back to the equation:

-(85b^2+255b)


We get rid of parentheses

-85b^2-255b=0

a = -85; b = -255; c = 0;
Δ = b2-4ac
Δ = -2552-4·(-85)·0
Δ = 65025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{65025}=255$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-255)-255}{2*-85}=\frac{0}{-170}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-255)+255}{2*-85}=\frac{510}{-170}
=-3
$