x(8/20)=3/20

Solution for x(8/20)=3/20 equation:

x(8/20)=3/20

We move all terms to the left:

x(8/20)-(3/20)=0

We add all the numbers together, and all the variables

x(+8/20)-(+3/20)=0

We multiply parentheses

8x^2-(+3/20)=0

We get rid of parentheses

8x^2-3/20=0

We multiply all the terms by the denominator


8x^2*20-3=0

Wy multiply elements

160x^2-3=0

a = 160; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·160·(-3)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{30}}{2*160}=\frac{0-8\sqrt{30}}{320}
=-\frac{8\sqrt{30}}{320}
=-\frac{\sqrt{30}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{30}}{2*160}=\frac{0+8\sqrt{30}}{320}
=\frac{8\sqrt{30}}{320}
=\frac{\sqrt{30}}{40}
$