3z(3z+11)=60

Solution for 3z(3z+11)=60 equation:

3z(3z+11)=60

We move all terms to the left:

3z(3z+11)-(60)=0

We multiply parentheses

9z^2+33z-60=0

a = 9; b = 33; c = -60;
Δ = b2-4ac
Δ = 332-4·9·(-60)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-57}{2*9}=\frac{-90}{18}
=-5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+57}{2*9}=\frac{24}{18}
=1+1/3
$