7x^2-1=11x

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

7x^2-1=11x

We move all terms to the left:

7x^2-1-(11x)=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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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