F(x)=-4x2+4x+15

Solution for F(x)=-4x2+4x+15 equation:

(F)=-4F^2+4F+15

We move all terms to the left:

(F)-(-4F^2+4F+15)=0

We get rid of parentheses

4F^2-4F+F-15=0

We add all the numbers together, and all the variables

4F^2-3F-15=0

a = 4; b = -3; c = -15;
Δ = b2-4ac
Δ = -32-4·4·(-15)
Δ = 249
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{-(-3)-\sqrt{249}}{2*4}=\frac{3-\sqrt{249}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{249}}{2*4}=\frac{3+\sqrt{249}}{8}
$