F(x)=-4x^2-24x+15

Solution for F(x)=-4x^2-24x+15 equation:

(F)=-4F^2-24F+15

We move all terms to the left:

(F)-(-4F^2-24F+15)=0

We get rid of parentheses

4F^2+24F+F-15=0

We add all the numbers together, and all the variables

4F^2+25F-15=0

a = 4; b = 25; c = -15;
Δ = b2-4ac
Δ = 252-4·4·(-15)
Δ = 865
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{-(25)-\sqrt{865}}{2*4}=\frac{-25-\sqrt{865}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{865}}{2*4}=\frac{-25+\sqrt{865}}{8}
$