x(8/5)=2/15

Solution for x(8/5)=2/15 equation:

x(8/5)=2/15

We move all terms to the left:

x(8/5)-(2/15)=0

We add all the numbers together, and all the variables

x(+8/5)-(+2/15)=0

We multiply parentheses

8x^2-(+2/15)=0

We get rid of parentheses

8x^2-2/15=0

We multiply all the terms by the denominator


8x^2*15-2=0

Wy multiply elements

120x^2-2=0

a = 120; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·120·(-2)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*120}=\frac{0-8\sqrt{15}}{240}
=-\frac{8\sqrt{15}}{240}
=-\frac{\sqrt{15}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*120}=\frac{0+8\sqrt{15}}{240}
=\frac{8\sqrt{15}}{240}
=\frac{\sqrt{15}}{30}
$