600=60x+5x^2/2

Solution for 600=60x+5x^2/2 equation:

600=60x+5x^2/2

We move all terms to the left:

600-(60x+5x^2/2)=0

We get rid of parentheses

-5x^2/2-60x+600=0

We multiply all the terms by the denominator


-5x^2-60x*2+600*2=0

We add all the numbers together, and all the variables

-5x^2-60x*2+1200=0

Wy multiply elements

-5x^2-120x+1200=0

a = -5; b = -120; c = +1200;
Δ = b2-4ac
Δ = -1202-4·(-5)·1200
Δ = 38400
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:

$\sqrt{\Delta}=\sqrt{38400}=\sqrt{6400*6}=\sqrt{6400}*\sqrt{6}=80\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-80\sqrt{6}}{2*-5}=\frac{120-80\sqrt{6}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+80\sqrt{6}}{2*-5}=\frac{120+80\sqrt{6}}{-10}
$