F(d)=0.77d^2-1.32d-9.31

Solution for F(d)=0.77d^2-1.32d-9.31 equation:

(F)=0.77F^2-1.32F-9.31

We move all terms to the left:

(F)-(0.77F^2-1.32F-9.31)=0

We get rid of parentheses

-0.77F^2+F+1.32F+9.31=0

We add all the numbers together, and all the variables

-0.77F^2+2.32F+9.31=0

a = -0.77; b = 2.32; c = +9.31;
Δ = b2-4ac
Δ = 2.322-4·(-0.77)·9.31
Δ = 34.0572
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{-(2.32)-\sqrt{34.0572}}{2*-0.77}=\frac{-2.32-\sqrt{34.0572}}{-1.54}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.32)+\sqrt{34.0572}}{2*-0.77}=\frac{-2.32+\sqrt{34.0572}}{-1.54}
$