Q(x)=7x^2-1

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

(Q)=7Q^2-1

We move all terms to the left:

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

We get rid of parentheses

-7Q^2+Q+1=0

a = -7; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-7)·1
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{29}}{2*-7}=\frac{-1-\sqrt{29}}{-14}
$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{29}}{2*-7}=\frac{-1+\sqrt{29}}{-14}
$