(1/2)x=2/15

Solution for (1/2)x=2/15 equation:

(1/2)x=2/15

We move all terms to the left:

(1/2)x-(2/15)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)x-(+2/15)=0

We multiply parentheses

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

We get rid of parentheses

x^2-2/15=0

We multiply all the terms by the denominator


x^2*15-2=0

Wy multiply elements

15x^2-2=0

a = 15; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·15·(-2)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*15}=\frac{0-2\sqrt{30}}{30}
=-\frac{2\sqrt{30}}{30}
=-\frac{\sqrt{30}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*15}=\frac{0+2\sqrt{30}}{30}
=\frac{2\sqrt{30}}{30}
=\frac{\sqrt{30}}{15}
$