3z(2z+11)=11

Solution for 3z(2z+11)=11 equation:

3z(2z+11)=11

We move all terms to the left:

3z(2z+11)-(11)=0

We multiply parentheses

6z^2+33z-11=0

a = 6; b = 33; c = -11;
Δ = b2-4ac
Δ = 332-4·6·(-11)
Δ = 1353
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{1353}}{2*6}=\frac{-33-\sqrt{1353}}{12}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1353}}{2*6}=\frac{-33+\sqrt{1353}}{12}
$