(13/6)x=5/3

Solution for (13/6)x=5/3 equation:

(13/6)x=5/3

We move all terms to the left:

(13/6)x-(5/3)=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+13/6)x-(+5/3)=0

We multiply parentheses

13x^2-(+5/3)=0

We get rid of parentheses

13x^2-5/3=0

We multiply all the terms by the denominator


13x^2*3-5=0

Wy multiply elements

39x^2-5=0

a = 39; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·39·(-5)
Δ = 780
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:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{195}}{2*39}=\frac{0-2\sqrt{195}}{78}
=-\frac{2\sqrt{195}}{78}
=-\frac{\sqrt{195}}{39}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{195}}{2*39}=\frac{0+2\sqrt{195}}{78}
=\frac{2\sqrt{195}}{78}
=\frac{\sqrt{195}}{39}
$