60=0.5x^2+2x

Solution for 60=0.5x^2+2x equation:

60=0.5x^2+2x

We move all terms to the left:

60-(0.5x^2+2x)=0

We get rid of parentheses

-0.5x^2-2x+60=0

a = -0.5; b = -2; c = +60;
Δ = b2-4ac
Δ = -22-4·(-0.5)·60
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*-0.5}=\frac{2-2\sqrt{31}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*-0.5}=\frac{2+2\sqrt{31}}{-1}
$