2b^2-14b+11=-3b-1

Solution for 2b^2-14b+11=-3b-1 equation:

2b^2-14b+11=-3b-1

We move all terms to the left:

2b^2-14b+11-(-3b-1)=0

We get rid of parentheses

2b^2-14b+3b+1+11=0

We add all the numbers together, and all the variables

2b^2-11b+12=0

a = 2; b = -11; c = +12;
Δ = b2-4ac
Δ = -112-4·2·12
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*2}=\frac{6}{4}
=1+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*2}=\frac{16}{4}
=4
$