F(t)=45/4t-31

Solution for F(t)=45/4t-31 equation:

(F)=45/4F-31

We move all terms to the left:

(F)-(45/4F-31)=0


Domain of the equation: 4F-31)!=0

F∈R


We get rid of parentheses

F-45/4F+31=0

We multiply all the terms by the denominator


F*4F+31*4F-45=0

Wy multiply elements

4F^2+124F-45=0

a = 4; b = 124; c = -45;
Δ = b2-4ac
Δ = 1242-4·4·(-45)
Δ = 16096
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:

$\sqrt{\Delta}=\sqrt{16096}=\sqrt{16*1006}=\sqrt{16}*\sqrt{1006}=4\sqrt{1006}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-4\sqrt{1006}}{2*4}=\frac{-124-4\sqrt{1006}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+4\sqrt{1006}}{2*4}=\frac{-124+4\sqrt{1006}}{8}
$