F(2a)=7-(2a)^2

Solution for F(2a)=7-(2a)^2 equation:

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

We move all terms to the left:

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

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

We get rid of parentheses

2F^2+2F-7=0

a = 2; b = 2; c = -7;
Δ = b2-4ac
Δ = 22-4·2·(-7)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{15}}{2*2}=\frac{-2-2\sqrt{15}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{15}}{2*2}=\frac{-2+2\sqrt{15}}{4}
$