F(x)=-0.1x^2+0.7x+7

Solution for F(x)=-0.1x^2+0.7x+7 equation:

(F)=-0.1F^2+0.7F+7

We move all terms to the left:

(F)-(-0.1F^2+0.7F+7)=0

We get rid of parentheses

0.1F^2-0.7F+F-7=0

We add all the numbers together, and all the variables

0.1F^2+0.3F-7=0

a = 0.1; b = 0.3; c = -7;
Δ = b2-4ac
Δ = 0.32-4·0.1·(-7)
Δ = 2.89
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{-(0.3)-\sqrt{2.89}}{2*0.1}=\frac{-0.3-\sqrt{2.89}}{0.2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.3)+\sqrt{2.89}}{2*0.1}=\frac{-0.3+\sqrt{2.89}}{0.2}
$