(18z+21)(10z+45)=180

Solution for (18z+21)(10z+45)=180 equation:

(18z+21)(10z+45)=180

We move all terms to the left:

(18z+21)(10z+45)-(180)=0

We multiply parentheses ..

(+180z^2+810z+210z+945)-180=0

We get rid of parentheses

180z^2+810z+210z+945-180=0

We add all the numbers together, and all the variables

180z^2+1020z+765=0

a = 180; b = 1020; c = +765;
Δ = b2-4ac
Δ = 10202-4·180·765
Δ = 489600
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:

$\sqrt{\Delta}=\sqrt{489600}=\sqrt{14400*34}=\sqrt{14400}*\sqrt{34}=120\sqrt{34}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1020)-120\sqrt{34}}{2*180}=\frac{-1020-120\sqrt{34}}{360}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1020)+120\sqrt{34}}{2*180}=\frac{-1020+120\sqrt{34}}{360}
$