5n(n+28)=50

Solution for 5n(n+28)=50 equation:

5n(n+28)=50

We move all terms to the left:

5n(n+28)-(50)=0

We multiply parentheses

5n^2+140n-50=0

a = 5; b = 140; c = -50;
Δ = b2-4ac
Δ = 1402-4·5·(-50)
Δ = 20600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20600}=\sqrt{100*206}=\sqrt{100}*\sqrt{206}=10\sqrt{206}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-10\sqrt{206}}{2*5}=\frac{-140-10\sqrt{206}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+10\sqrt{206}}{2*5}=\frac{-140+10\sqrt{206}}{10}
$