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

x^2+144x-2400=0

a = 1; b = 144; c = -2400;
Δ = b2-4ac
Δ = 1442-4·1·(-2400)
Δ = 30336
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:

$\sqrt{\Delta}=\sqrt{30336}=\sqrt{64*474}=\sqrt{64}*\sqrt{474}=8\sqrt{474}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-8\sqrt{474}}{2*1}=\frac{-144-8\sqrt{474}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+8\sqrt{474}}{2*1}=\frac{-144+8\sqrt{474}}{2}
$