5x^2-1-11x=0

Solution for 5x^2-1-11x=0 equation:

5x^2-1-11x=0

a = 5; b = -11; c = -1;
Δ = b2-4ac
Δ = -112-4·5·(-1)
Δ = 141
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{141}}{2*5}=\frac{11-\sqrt{141}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{141}}{2*5}=\frac{11+\sqrt{141}}{10}
$