x2+69x=-684

Solution for x2+69x=-684 equation:

x2+69x=-684

We move all terms to the left:

x2+69x-(-684)=0

We add all the numbers together, and all the variables

x^2+69x+684=0

a = 1; b = 69; c = +684;
Δ = b2-4ac
Δ = 692-4·1·684
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-45}{2*1}=\frac{-114}{2}
=-57
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+45}{2*1}=\frac{-24}{2}
=-12
$