4b^2+11b=5

Solution for 4b^2+11b=5 equation:

4b^2+11b=5

We move all terms to the left:

4b^2+11b-(5)=0

a = 4; b = 11; c = -5;
Δ = b2-4ac
Δ = 112-4·4·(-5)
Δ = 201
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{201}}{2*4}=\frac{-11-\sqrt{201}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{201}}{2*4}=\frac{-11+\sqrt{201}}{8}
$