F(x)=2x^2+24x+22

Solution for F(x)=2x^2+24x+22 equation:

(F)=2F^2+24F+22

We move all terms to the left:

(F)-(2F^2+24F+22)=0

We get rid of parentheses

-2F^2+F-24F-22=0

We add all the numbers together, and all the variables

-2F^2-23F-22=0

a = -2; b = -23; c = -22;
Δ = b2-4ac
Δ = -232-4·(-2)·(-22)
Δ = 353
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{-(-23)-\sqrt{353}}{2*-2}=\frac{23-\sqrt{353}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{353}}{2*-2}=\frac{23+\sqrt{353}}{-4}
$