35+11x-x^2=0

Solution for 35+11x-x^2=0 equation:

35+11x-x^2=0

We add all the numbers together, and all the variables

-1x^2+11x+35=0

a = -1; b = 11; c = +35;
Δ = b2-4ac
Δ = 112-4·(-1)·35
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{29}}{2*-1}=\frac{-11-3\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{29}}{2*-1}=\frac{-11+3\sqrt{29}}{-2}
$