(z-15)(2z)=180

Solution for (z-15)(2z)=180 equation:

(z-15)(2z)=180

We move all terms to the left:

(z-15)(2z)-(180)=0

We multiply parentheses

2z^2-30z-180=0

a = 2; b = -30; c = -180;
Δ = b2-4ac
Δ = -302-4·2·(-180)
Δ = 2340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{65}}{2*2}=\frac{30-6\sqrt{65}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{65}}{2*2}=\frac{30+6\sqrt{65}}{4}
$