F(x)=-2x^2-28x-90

Solution for F(x)=-2x^2-28x-90 equation:

(F)=-2F^2-28F-90

We move all terms to the left:

(F)-(-2F^2-28F-90)=0

We get rid of parentheses

2F^2+28F+F+90=0

We add all the numbers together, and all the variables

2F^2+29F+90=0

a = 2; b = 29; c = +90;
Δ = b2-4ac
Δ = 292-4·2·90
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-11}{2*2}=\frac{-40}{4}
=-10
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+11}{2*2}=\frac{-18}{4}
=-4+1/2
$