H(x)=7x^2-x-1

Solution for H(x)=7x^2-x-1 equation:

(H)=7H^2-H-1

We move all terms to the left:

(H)-(7H^2-H-1)=0

We get rid of parentheses

-7H^2+H+H+1=0

We add all the numbers together, and all the variables

-7H^2+2H+1=0

a = -7; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-7)·1
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{-(2)-4\sqrt{2}}{2*-7}=\frac{-2-4\sqrt{2}}{-14}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{2}}{2*-7}=\frac{-2+4\sqrt{2}}{-14}
$