H(x)=x2+9x+14

Solution for H(x)=x2+9x+14 equation:

(H)=H2+9H+14

We move all terms to the left:

(H)-(H2+9H+14)=0

We add all the numbers together, and all the variables

-(+H^2+9H+14)+H=0

We get rid of parentheses

-H^2-9H+H-14=0

We add all the numbers together, and all the variables

-1H^2-8H-14=0

a = -1; b = -8; c = -14;
Δ = b2-4ac
Δ = -82-4·(-1)·(-14)
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{2}}{2*-1}=\frac{8-2\sqrt{2}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{2}}{2*-1}=\frac{8+2\sqrt{2}}{-2}
$