30/100*x=20

Solution for 30/100*x=20 equation:

30/100*x=20

We move all terms to the left:

30/100*x-(20)=0


Domain of the equation: 100*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-20*100*x+30=0

Wy multiply elements

-2000x*x+30=0

Wy multiply elements

-2000x^2+30=0

a = -2000; b = 0; c = +30;
Δ = b2-4ac
Δ = 02-4·(-2000)·30
Δ = 240000
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:

$\sqrt{\Delta}=\sqrt{240000}=\sqrt{40000*6}=\sqrt{40000}*\sqrt{6}=200\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{6}}{2*-2000}=\frac{0-200\sqrt{6}}{-4000}
=-\frac{200\sqrt{6}}{-4000}
=-\frac{\sqrt{6}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{6}}{2*-2000}=\frac{0+200\sqrt{6}}{-4000}
=\frac{200\sqrt{6}}{-4000}
=\frac{\sqrt{6}}{-20}
$