60=12(5+z)z=

Solution for 60=12(5+z)z= equation:

60=12(5+z)z=

We move all terms to the left:

60-(12(5+z)z)=0

We add all the numbers together, and all the variables

-(12(z+5)z)+60=0


We calculate terms in parentheses: -(12(z+5)z), so:

12(z+5)z

We multiply parentheses

12z^2+60z

Back to the equation:

-(12z^2+60z)


We get rid of parentheses

-12z^2-60z+60=0

a = -12; b = -60; c = +60;
Δ = b2-4ac
Δ = -602-4·(-12)·60
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-36\sqrt{5}}{2*-12}=\frac{60-36\sqrt{5}}{-24}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+36\sqrt{5}}{2*-12}=\frac{60+36\sqrt{5}}{-24}
$