F(x)=4.9x^2+12x+2.5

Solution for F(x)=4.9x^2+12x+2.5 equation:

(F)=4.9F^2+12F+2.5

We move all terms to the left:

(F)-(4.9F^2+12F+2.5)=0

We get rid of parentheses

-4.9F^2+F-12F-2.5=0

We add all the numbers together, and all the variables

-4.9F^2-11F-2.5=0

a = -4.9; b = -11; c = -2.5;
Δ = b2-4ac
Δ = -112-4·(-4.9)·(-2.5)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-6\sqrt{2}}{2*-4.9}=\frac{11-6\sqrt{2}}{-9.8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+6\sqrt{2}}{2*-4.9}=\frac{11+6\sqrt{2}}{-9.8}
$