5b^2-11b-1=-3

Solution for 5b^2-11b-1=-3 equation:

5b^2-11b-1=-3

We move all terms to the left:

5b^2-11b-1-(-3)=0

We add all the numbers together, and all the variables

5b^2-11b+2=0

a = 5; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·5·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-9}{2*5}=\frac{2}{10}
=1/5
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+9}{2*5}=\frac{20}{10}
=2
$