10x*20x/120=200

Solution for 10x*20x/120=200 equation:

10x*20x/120=200

We move all terms to the left:

10x*20x/120-(200)=0

We multiply all the terms by the denominator


10x*20x-200*120=0

We add all the numbers together, and all the variables

10x*20x-24000=0

Wy multiply elements

200x^2-24000=0

a = 200; b = 0; c = -24000;
Δ = b2-4ac
Δ = 02-4·200·(-24000)
Δ = 19200000
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:

$\sqrt{\Delta}=\sqrt{19200000}=\sqrt{640000*30}=\sqrt{640000}*\sqrt{30}=800\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-800\sqrt{30}}{2*200}=\frac{0-800\sqrt{30}}{400}
=-\frac{800\sqrt{30}}{400}
=-2\sqrt{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+800\sqrt{30}}{2*200}=\frac{0+800\sqrt{30}}{400}
=\frac{800\sqrt{30}}{400}
=2\sqrt{30}
$