60=l(l-8)

Solution for 60=l(l-8) equation:

60=l(l-8)

We move all terms to the left:

60-(l(l-8))=0


We calculate terms in parentheses: -(l(l-8)), so:

l(l-8)

We multiply parentheses

l^2-8l

Back to the equation:

-(l^2-8l)


We get rid of parentheses

-l^2+8l+60=0

We add all the numbers together, and all the variables

-1l^2+8l+60=0

a = -1; b = 8; c = +60;
Δ = b2-4ac
Δ = 82-4·(-1)·60
Δ = 304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{19}}{2*-1}=\frac{-8-4\sqrt{19}}{-2}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{19}}{2*-1}=\frac{-8+4\sqrt{19}}{-2}
$