F(x)=-3x^2-x+7

Solution for F(x)=-3x^2-x+7 equation:

(F)=-3F^2-F+7

We move all terms to the left:

(F)-(-3F^2-F+7)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

3F^2+2F-7=0

a = 3; b = 2; c = -7;
Δ = b2-4ac
Δ = 22-4·3·(-7)
Δ = 88
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{22}}{2*3}=\frac{-2-2\sqrt{22}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{22}}{2*3}=\frac{-2+2\sqrt{22}}{6}
$