60=40x+5x^2

Solution for 60=40x+5x^2 equation:

60=40x+5x^2

We move all terms to the left:

60-(40x+5x^2)=0

We get rid of parentheses

-5x^2-40x+60=0

a = -5; b = -40; c = +60;
Δ = b2-4ac
Δ = -402-4·(-5)·60
Δ = 2800
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:

$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{7}}{2*-5}=\frac{40-20\sqrt{7}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{7}}{2*-5}=\frac{40+20\sqrt{7}}{-10}
$