F(x)=-0.2x^2+1.7x+5.3

Solution for F(x)=-0.2x^2+1.7x+5.3 equation:

(F)=-0.2F^2+1.7F+5.3

We move all terms to the left:

(F)-(-0.2F^2+1.7F+5.3)=0

We get rid of parentheses

0.2F^2-1.7F+F-5.3=0

We add all the numbers together, and all the variables

0.2F^2-0.7F-5.3=0

a = 0.2; b = -0.7; c = -5.3;
Δ = b2-4ac
Δ = -0.72-4·0.2·(-5.3)
Δ = 4.73
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{-(-0.7)-\sqrt{4.73}}{2*0.2}=\frac{0.7-\sqrt{4.73}}{0.4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.7)+\sqrt{4.73}}{2*0.2}=\frac{0.7+\sqrt{4.73}}{0.4}
$