F(6)=4x^2-7

Solution for F(6)=4x^2-7 equation:

(6)=4F^2-7

We move all terms to the left:

(6)-(4F^2-7)=0

We get rid of parentheses

-4F^2+7+6=0

We add all the numbers together, and all the variables

-4F^2+13=0

a = -4; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-4)·13
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{13}}{2*-4}=\frac{0-4\sqrt{13}}{-8}
=-\frac{4\sqrt{13}}{-8}
=-\frac{\sqrt{13}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{13}}{2*-4}=\frac{0+4\sqrt{13}}{-8}
=\frac{4\sqrt{13}}{-8}
=\frac{\sqrt{13}}{-2}
$