(10*2x)(30*2x)=800

Solution for (10*2x)(30*2x)=800 equation:

(10*2x)(30*2x)=800

We move all terms to the left:

(10*2x)(30*2x)-(800)=0

We add all the numbers together, and all the variables

(+10*2x)(+30*2x)-800=0

We multiply parentheses ..

(+1200x^2)-800=0

We get rid of parentheses

1200x^2-800=0

a = 1200; b = 0; c = -800;
Δ = b2-4ac
Δ = 02-4·1200·(-800)
Δ = 3840000
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:

$\sqrt{\Delta}=\sqrt{3840000}=\sqrt{640000*6}=\sqrt{640000}*\sqrt{6}=800\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-800\sqrt{6}}{2*1200}=\frac{0-800\sqrt{6}}{2400}
=-\frac{800\sqrt{6}}{2400}
=-\frac{\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+800\sqrt{6}}{2*1200}=\frac{0+800\sqrt{6}}{2400}
=\frac{800\sqrt{6}}{2400}
=\frac{\sqrt{6}}{3}
$