x^2+28x=-17

Solution for x^2+28x=-17 equation:

x^2+28x=-17

We move all terms to the left:

x^2+28x-(-17)=0

We add all the numbers together, and all the variables

x^2+28x+17=0

a = 1; b = 28; c = +17;
Δ = b2-4ac
Δ = 282-4·1·17
Δ = 716
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:

$\sqrt{\Delta}=\sqrt{716}=\sqrt{4*179}=\sqrt{4}*\sqrt{179}=2\sqrt{179}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{179}}{2*1}=\frac{-28-2\sqrt{179}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{179}}{2*1}=\frac{-28+2\sqrt{179}}{2}
$