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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2F^2-9F-7=0

a = -2; b = -9; c = -7;
Δ = b2-4ac
Δ = -92-4·(-2)·(-7)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5}{2*-2}=\frac{4}{-4}
=-1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5}{2*-2}=\frac{14}{-4}
=-3+1/2
$