(k/2)(1+k)=171

Solution for (k/2)(1+k)=171 equation:

(k/2)(1+k)=171

We move all terms to the left:

(k/2)(1+k)-(171)=0


Domain of the equation: 2)(1+k)!=0

k∈R


We add all the numbers together, and all the variables

(+k/2)(k+1)-171=0

We multiply parentheses ..

(+k^2+k)-171=0

We get rid of parentheses

k^2+k-171=0

a = 1; b = 1; c = -171;
Δ = b2-4ac
Δ = 12-4·1·(-171)
Δ = 685
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{685}}{2*1}=\frac{-1-\sqrt{685}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{685}}{2*1}=\frac{-1+\sqrt{685}}{2}
$