x*x*20/100=180

Solution for x*x*20/100=180 equation:

x*x*20/100=180

We move all terms to the left:

x*x*20/100-(180)=0

We multiply all the terms by the denominator


x*x*20-180*100=0

We add all the numbers together, and all the variables

x*x*20-18000=0

Wy multiply elements

20x^2*2-18000=0

Wy multiply elements

40x^2-18000=0

a = 40; b = 0; c = -18000;
Δ = b2-4ac
Δ = 02-4·40·(-18000)
Δ = 2880000
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:

$\sqrt{\Delta}=\sqrt{2880000}=\sqrt{1440000*2}=\sqrt{1440000}*\sqrt{2}=1200\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1200\sqrt{2}}{2*40}=\frac{0-1200\sqrt{2}}{80}
=-\frac{1200\sqrt{2}}{80}
=-15\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1200\sqrt{2}}{2*40}=\frac{0+1200\sqrt{2}}{80}
=\frac{1200\sqrt{2}}{80}
=15\sqrt{2}
$