x2+5x=550

Solution for x2+5x=550 equation:

x2+5x=550

We move all terms to the left:

x2+5x-(550)=0

We add all the numbers together, and all the variables

x^2+5x-550=0

a = 1; b = 5; c = -550;
Δ = b2-4ac
Δ = 52-4·1·(-550)
Δ = 2225
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:

$\sqrt{\Delta}=\sqrt{2225}=\sqrt{25*89}=\sqrt{25}*\sqrt{89}=5\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{89}}{2*1}=\frac{-5-5\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{89}}{2*1}=\frac{-5+5\sqrt{89}}{2}
$