5z(z-32)=11

Solution for 5z(z-32)=11 equation:

5z(z-32)=11

We move all terms to the left:

5z(z-32)-(11)=0

We multiply parentheses

5z^2-160z-11=0

a = 5; b = -160; c = -11;
Δ = b2-4ac
Δ = -1602-4·5·(-11)
Δ = 25820
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:

$\sqrt{\Delta}=\sqrt{25820}=\sqrt{4*6455}=\sqrt{4}*\sqrt{6455}=2\sqrt{6455}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-2\sqrt{6455}}{2*5}=\frac{160-2\sqrt{6455}}{10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+2\sqrt{6455}}{2*5}=\frac{160+2\sqrt{6455}}{10}
$