F(x)=24x^2-46+21

Solution for F(x)=24x^2-46+21 equation:

(F)=24F^2-46+21

We move all terms to the left:

(F)-(24F^2-46+21)=0

We get rid of parentheses

-24F^2+F+46-21=0

We add all the numbers together, and all the variables

-24F^2+F+25=0

a = -24; b = 1; c = +25;
Δ = b2-4ac
Δ = 12-4·(-24)·25
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-49}{2*-24}=\frac{-50}{-48}
=1+1/24
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+49}{2*-24}=\frac{48}{-48}
=-1
$