F(t)=t^2-4t-7

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1F^2+5F+7=0

a = -1; b = 5; c = +7;
Δ = b2-4ac
Δ = 52-4·(-1)·7
Δ = 53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{53}}{2*-1}=\frac{-5-\sqrt{53}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{53}}{2*-1}=\frac{-5+\sqrt{53}}{-2}
$