0=-x^2+12x+35

Solution for 0=-x^2+12x+35 equation:

0=-x^2+12x+35

We move all terms to the left:

0-(-x^2+12x+35)=0

We add all the numbers together, and all the variables

-(-x^2+12x+35)=0

We get rid of parentheses

x^2-12x-35=0

a = 1; b = -12; c = -35;
Δ = b2-4ac
Δ = -122-4·1·(-35)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{71}}{2*1}=\frac{12-2\sqrt{71}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{71}}{2*1}=\frac{12+2\sqrt{71}}{2}
$