F(x)=2x2+12x+13

Solution for F(x)=2x2+12x+13 equation:

(F)=2F^2+12F+13

We move all terms to the left:

(F)-(2F^2+12F+13)=0

We get rid of parentheses

-2F^2+F-12F-13=0

We add all the numbers together, and all the variables

-2F^2-11F-13=0

a = -2; b = -11; c = -13;
Δ = b2-4ac
Δ = -112-4·(-2)·(-13)
Δ = 17
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{-(-11)-\sqrt{17}}{2*-2}=\frac{11-\sqrt{17}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{17}}{2*-2}=\frac{11+\sqrt{17}}{-4}
$