(7z-3)(5z-6)=180

Solution for (7z-3)(5z-6)=180 equation:

(7z-3)(5z-6)=180

We move all terms to the left:

(7z-3)(5z-6)-(180)=0

We multiply parentheses ..

(+35z^2-42z-15z+18)-180=0

We get rid of parentheses

35z^2-42z-15z+18-180=0

We add all the numbers together, and all the variables

35z^2-57z-162=0

a = 35; b = -57; c = -162;
Δ = b2-4ac
Δ = -572-4·35·(-162)
Δ = 25929
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:

$\sqrt{\Delta}=\sqrt{25929}=\sqrt{9*2881}=\sqrt{9}*\sqrt{2881}=3\sqrt{2881}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-3\sqrt{2881}}{2*35}=\frac{57-3\sqrt{2881}}{70}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+3\sqrt{2881}}{2*35}=\frac{57+3\sqrt{2881}}{70}
$