7b^2-1=11b

Solution for 7b^2-1=11b equation:

7b^2-1=11b

We move all terms to the left:

7b^2-1-(11b)=0

a = 7; b = -11; c = -1;
Δ = b2-4ac
Δ = -112-4·7·(-1)
Δ = 149
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{149}}{2*7}=\frac{11-\sqrt{149}}{14}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{149}}{2*7}=\frac{11+\sqrt{149}}{14}
$