x(10/3)=2/9

Solution for x(10/3)=2/9 equation:

x(10/3)=2/9

We move all terms to the left:

x(10/3)-(2/9)=0

We add all the numbers together, and all the variables

x(+10/3)-(+2/9)=0

We multiply parentheses

10x^2-(+2/9)=0

We get rid of parentheses

10x^2-2/9=0

We multiply all the terms by the denominator


10x^2*9-2=0

Wy multiply elements

90x^2-2=0

a = 90; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·90·(-2)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*90}=\frac{0-12\sqrt{5}}{180}
=-\frac{12\sqrt{5}}{180}
=-\frac{\sqrt{5}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*90}=\frac{0+12\sqrt{5}}{180}
=\frac{12\sqrt{5}}{180}
=\frac{\sqrt{5}}{15}
$