397.5=60x+5x^2/2

Solution for 397.5=60x+5x^2/2 equation:

397.5=60x+5x^2/2

We move all terms to the left:

397.5-(60x+5x^2/2)=0

We get rid of parentheses

-5x^2/2-60x+397.5=0

We multiply all the terms by the denominator


-5x^2-60x*2+(397.5)*2=0

We add all the numbers together, and all the variables

-5x^2-60x*2+795=0

Wy multiply elements

-5x^2-120x+795=0

a = -5; b = -120; c = +795;
Δ = b2-4ac
Δ = -1202-4·(-5)·795
Δ = 30300
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:

$\sqrt{\Delta}=\sqrt{30300}=\sqrt{100*303}=\sqrt{100}*\sqrt{303}=10\sqrt{303}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-10\sqrt{303}}{2*-5}=\frac{120-10\sqrt{303}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+10\sqrt{303}}{2*-5}=\frac{120+10\sqrt{303}}{-10}
$