(2z-3)(5z-6)=180

Solution for (2z-3)(5z-6)=180 equation:

(2z-3)(5z-6)=180

We move all terms to the left:

(2z-3)(5z-6)-(180)=0

We multiply parentheses ..

(+10z^2-12z-15z+18)-180=0

We get rid of parentheses

10z^2-12z-15z+18-180=0

We add all the numbers together, and all the variables

10z^2-27z-162=0

a = 10; b = -27; c = -162;
Δ = b2-4ac
Δ = -272-4·10·(-162)
Δ = 7209
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:

$\sqrt{\Delta}=\sqrt{7209}=\sqrt{81*89}=\sqrt{81}*\sqrt{89}=9\sqrt{89}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9\sqrt{89}}{2*10}=\frac{27-9\sqrt{89}}{20}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9\sqrt{89}}{2*10}=\frac{27+9\sqrt{89}}{20}
$