-x^2/3+32x/3=60

Solution for -x^2/3+32x/3=60 equation:

-x^2/3+32x/3=60

We move all terms to the left:

-x^2/3+32x/3-(60)=0

We multiply all the terms by the denominator


-x^2+32x-60*3=0

We add all the numbers together, and all the variables

-1x^2+32x-180=0

a = -1; b = 32; c = -180;
Δ = b2-4ac
Δ = 322-4·(-1)·(-180)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{19}}{2*-1}=\frac{-32-4\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{19}}{2*-1}=\frac{-32+4\sqrt{19}}{-2}
$