F(x)=3x^2-6x-15

Solution for F(x)=3x^2-6x-15 equation:

(F)=3F^2-6F-15

We move all terms to the left:

(F)-(3F^2-6F-15)=0

We get rid of parentheses

-3F^2+F+6F+15=0

We add all the numbers together, and all the variables

-3F^2+7F+15=0

a = -3; b = 7; c = +15;
Δ = b2-4ac
Δ = 72-4·(-3)·15
Δ = 229
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{-(7)-\sqrt{229}}{2*-3}=\frac{-7-\sqrt{229}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{229}}{2*-3}=\frac{-7+\sqrt{229}}{-6}
$