-x^2-196+35x=0

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

-x^2-196+35x=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 = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-21}{2*-1}=\frac{-56}{-2}
=+28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+21}{2*-1}=\frac{-14}{-2}
=+7
$