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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(3F^2+7F+7(-2)), so:

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

We add all the numbers together, and all the variables

3F^2+7F-14

Back to the equation:

-(3F^2+7F-14)


We get rid of parentheses

-3F^2+F-7F+14=0

We add all the numbers together, and all the variables

-3F^2-6F+14=0

a = -3; b = -6; c = +14;
Δ = b2-4ac
Δ = -62-4·(-3)·14
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{51}}{2*-3}=\frac{6-2\sqrt{51}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{51}}{2*-3}=\frac{6+2\sqrt{51}}{-6}
$