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

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

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

We move all terms to the left:

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

We get rid of parentheses

-77H^2+7H+1=0

a = -77; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-77)·1
Δ = 357
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{357}}{2*-77}=\frac{-7-\sqrt{357}}{-154}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{357}}{2*-77}=\frac{-7+\sqrt{357}}{-154}
$