-x*x/2+72x-1200=0

Solution for -x*x/2+72x-1200=0 equation:

-x*x/2+72x-1200=0

We add all the numbers together, and all the variables

72x-x*x/2-1200=0

We multiply all the terms by the denominator


72x*2-x*x-1200*2=0

We add all the numbers together, and all the variables

72x*2-x*x-2400=0

Wy multiply elements

-1x^2+144x-2400=0

a = -1; b = 144; c = -2400;
Δ = b2-4ac
Δ = 1442-4·(-1)·(-2400)
Δ = 11136
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:

$\sqrt{\Delta}=\sqrt{11136}=\sqrt{64*174}=\sqrt{64}*\sqrt{174}=8\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-8\sqrt{174}}{2*-1}=\frac{-144-8\sqrt{174}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+8\sqrt{174}}{2*-1}=\frac{-144+8\sqrt{174}}{-2}
$