60=2x(x+1)

Solution for 60=2x(x+1) equation:

60=2x(x+1)

We move all terms to the left:

60-(2x(x+1))=0


We calculate terms in parentheses: -(2x(x+1)), so:

2x(x+1)

We multiply parentheses

2x^2+2x

Back to the equation:

-(2x^2+2x)


We get rid of parentheses

-2x^2-2x+60=0

a = -2; b = -2; c = +60;
Δ = b2-4ac
Δ = -22-4·(-2)·60
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*-2}=\frac{24}{-4}
=-6
$