n(n+3)=154

Solution for n(n+3)=154 equation:

n(n+3)=154

We move all terms to the left:

n(n+3)-(154)=0

We multiply parentheses

n^2+3n-154=0

a = 1; b = 3; c = -154;
Δ = b2-4ac
Δ = 32-4·1·(-154)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-25}{2*1}=\frac{-28}{2}
=-14
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+25}{2*1}=\frac{22}{2}
=11
$