H(x)=x^2-15x+56

Solution for H(x)=x^2-15x+56 equation:

(H)=H^2-15H+56

We move all terms to the left:

(H)-(H^2-15H+56)=0

We get rid of parentheses

-H^2+H+15H-56=0

We add all the numbers together, and all the variables

-1H^2+16H-56=0

a = -1; b = 16; c = -56;
Δ = b2-4ac
Δ = 162-4·(-1)·(-56)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{2}}{2*-1}=\frac{-16-4\sqrt{2}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{2}}{2*-1}=\frac{-16+4\sqrt{2}}{-2}
$