x*(30/100)=180000

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Solution for x*(30/100)=180000 equation:



x*(30/100)=180000
We move all terms to the left:
x*(30/100)-(180000)=0
We add all the numbers together, and all the variables
x*(+30/100)-180000=0
We multiply parentheses
30x^2-180000=0
a = 30; b = 0; c = -180000;
Δ = b2-4ac
Δ = 02-4·30·(-180000)
Δ = 21600000
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:
$\sqrt{\Delta}=\sqrt{21600000}=\sqrt{1440000*15}=\sqrt{1440000}*\sqrt{15}=1200\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1200\sqrt{15}}{2*30}=\frac{0-1200\sqrt{15}}{60} =-\frac{1200\sqrt{15}}{60} =-20\sqrt{15} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1200\sqrt{15}}{2*30}=\frac{0+1200\sqrt{15}}{60} =\frac{1200\sqrt{15}}{60} =20\sqrt{15} $

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