b(b+3)/2=17

Solution for b(b+3)/2=17 equation:

b(b+3)/2=17

We move all terms to the left:

b(b+3)/2-(17)=0

We multiply all the terms by the denominator


b(b+3)-17*2=0

We add all the numbers together, and all the variables

b(b+3)-34=0

We multiply parentheses

b^2+3b-34=0

a = 1; b = 3; c = -34;
Δ = b2-4ac
Δ = 32-4·1·(-34)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{145}}{2*1}=\frac{-3-\sqrt{145}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{145}}{2*1}=\frac{-3+\sqrt{145}}{2}
$