F(4)=2x^2-30

Solution for F(4)=2x^2-30 equation:

(4)=2F^2-30

We move all terms to the left:

(4)-(2F^2-30)=0

We get rid of parentheses

-2F^2+30+4=0

We add all the numbers together, and all the variables

-2F^2+34=0

a = -2; b = 0; c = +34;
Δ = b2-4ac
Δ = 02-4·(-2)·34
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{17}}{2*-2}=\frac{0-4\sqrt{17}}{-4}
=-\frac{4\sqrt{17}}{-4}
=-\frac{\sqrt{17}}{-1}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{17}}{2*-2}=\frac{0+4\sqrt{17}}{-4}
=\frac{4\sqrt{17}}{-4}
=\frac{\sqrt{17}}{-1}
$