-x^2+35x+196=0

Solution for -x^2+35x+196=0 equation:

-x^2+35x+196=0

We add all the numbers together, and all the variables

-1x^2+35x+196=0

a = -1; b = 35; c = +196;
Δ = b2-4ac
Δ = 352-4·(-1)·196
Δ = 2009
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:

$\sqrt{\Delta}=\sqrt{2009}=\sqrt{49*41}=\sqrt{49}*\sqrt{41}=7\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-7\sqrt{41}}{2*-1}=\frac{-35-7\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+7\sqrt{41}}{2*-1}=\frac{-35+7\sqrt{41}}{-2}
$