(69x)+(-x2)=999

Solution for (69x)+(-x2)=999 equation:

(69x)+(-x2)=999

We move all terms to the left:

(69x)+(-x2)-(999)=0

We add all the numbers together, and all the variables

(-1x^2)+69x-999=0

We get rid of parentheses

-1x^2+69x-999=0

a = -1; b = 69; c = -999;
Δ = b2-4ac
Δ = 692-4·(-1)·(-999)
Δ = 765
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:

$\sqrt{\Delta}=\sqrt{765}=\sqrt{9*85}=\sqrt{9}*\sqrt{85}=3\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-3\sqrt{85}}{2*-1}=\frac{-69-3\sqrt{85}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+3\sqrt{85}}{2*-1}=\frac{-69+3\sqrt{85}}{-2}
$