4b^2-16b+11=4

Solution for 4b^2-16b+11=4 equation:

4b^2-16b+11=4

We move all terms to the left:

4b^2-16b+11-(4)=0

We add all the numbers together, and all the variables

4b^2-16b+7=0

a = 4; b = -16; c = +7;
Δ = b2-4ac
Δ = -162-4·4·7
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12}{2*4}=\frac{4}{8}
=1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12}{2*4}=\frac{28}{8}
=3+1/2
$