60=t(16+t)

Solution for 60=t(16+t) equation:

60=t(16+t)

We move all terms to the left:

60-(t(16+t))=0

We add all the numbers together, and all the variables

-(t(t+16))+60=0


We calculate terms in parentheses: -(t(t+16)), so:

t(t+16)

We multiply parentheses

t^2+16t

Back to the equation:

-(t^2+16t)


We get rid of parentheses

-t^2-16t+60=0

We add all the numbers together, and all the variables

-1t^2-16t+60=0

a = -1; b = -16; c = +60;
Δ = b2-4ac
Δ = -162-4·(-1)·60
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{31}}{2*-1}=\frac{16-4\sqrt{31}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{31}}{2*-1}=\frac{16+4\sqrt{31}}{-2}
$