F(r)=5r-7+2r^2

Solution for F(r)=5r-7+2r^2 equation:

(F)=5F-7+2F^2

We move all terms to the left:

(F)-(5F-7+2F^2)=0

We get rid of parentheses

-2F^2-5F+F+7=0

We add all the numbers together, and all the variables

-2F^2-4F+7=0

a = -2; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-2)·7
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{-(-4)-6\sqrt{2}}{2*-2}=\frac{4-6\sqrt{2}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{2}}{2*-2}=\frac{4+6\sqrt{2}}{-4}
$