F(x)=4x^2-48+7

Solution for F(x)=4x^2-48+7 equation:

(F)=4F^2-48+7

We move all terms to the left:

(F)-(4F^2-48+7)=0

We get rid of parentheses

-4F^2+F+48-7=0

We add all the numbers together, and all the variables

-4F^2+F+41=0

a = -4; b = 1; c = +41;
Δ = b2-4ac
Δ = 12-4·(-4)·41
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{73}}{2*-4}=\frac{-1-3\sqrt{73}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{73}}{2*-4}=\frac{-1+3\sqrt{73}}{-8}
$