H(x)=7x+x2

Solution for H(x)=7x+x2 equation:

(H)=7H+H2

We move all terms to the left:

(H)-(7H+H2)=0

We add all the numbers together, and all the variables

-(+7H+H^2)+H=0

We get rid of parentheses

-H^2-7H+H=0

We add all the numbers together, and all the variables

-1H^2-6H=0

a = -1; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-1)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-1}=\frac{0}{-2}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-1}=\frac{12}{-2}
=-6
$