F(x)=-2x^2-7x+10

Solution for F(x)=-2x^2-7x+10 equation:

(F)=-2F^2-7F+10

We move all terms to the left:

(F)-(-2F^2-7F+10)=0

We get rid of parentheses

2F^2+7F+F-10=0

We add all the numbers together, and all the variables

2F^2+8F-10=0

a = 2; b = 8; c = -10;
Δ = b2-4ac
Δ = 82-4·2·(-10)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12}{2*2}=\frac{-20}{4}
=-5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*2}=\frac{4}{4}
=1
$