F(x)=-2x^2+6x+36

Solution for F(x)=-2x^2+6x+36 equation:

(F)=-2F^2+6F+36

We move all terms to the left:

(F)-(-2F^2+6F+36)=0

We get rid of parentheses

2F^2-6F+F-36=0

We add all the numbers together, and all the variables

2F^2-5F-36=0

a = 2; b = -5; c = -36;
Δ = b2-4ac
Δ = -52-4·2·(-36)
Δ = 313
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{313}}{2*2}=\frac{5-\sqrt{313}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{313}}{2*2}=\frac{5+\sqrt{313}}{4}
$