F(t)=15t+7t^2-3

Solution for F(t)=15t+7t^2-3 equation:

(F)=15F+7F^2-3

We move all terms to the left:

(F)-(15F+7F^2-3)=0

We get rid of parentheses

-7F^2-15F+F+3=0

We add all the numbers together, and all the variables

-7F^2-14F+3=0

a = -7; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·(-7)·3
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{70}}{2*-7}=\frac{14-2\sqrt{70}}{-14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{70}}{2*-7}=\frac{14+2\sqrt{70}}{-14}
$