x^2+5x=221

Solution for x^2+5x=221 equation:

x^2+5x=221

We move all terms to the left:

x^2+5x-(221)=0

a = 1; b = 5; c = -221;
Δ = b2-4ac
Δ = 52-4·1·(-221)
Δ = 909
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{909}=\sqrt{9*101}=\sqrt{9}*\sqrt{101}=3\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{101}}{2*1}=\frac{-5-3\sqrt{101}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{101}}{2*1}=\frac{-5+3\sqrt{101}}{2}
$