(1/2)x+(1/5)=13

Solution for (1/2)x+(1/5)=13 equation:

(1/2)x+(1/5)=13

We move all terms to the left:

(1/2)x+(1/5)-(13)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(1/2)x-13+(1/5)=0

We add all the numbers together, and all the variables

(+1/2)x-13+(+1/5)=0

We multiply parentheses

x^2-13+(+1/5)=0

We get rid of parentheses

x^2-13+1/5=0

We multiply all the terms by the denominator


x^2*5+1-13*5=0

We add all the numbers together, and all the variables

x^2*5-64=0

Wy multiply elements

5x^2-64=0

a = 5; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·5·(-64)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{5}}{2*5}=\frac{0-16\sqrt{5}}{10}
=-\frac{16\sqrt{5}}{10}
=-\frac{8\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{5}}{2*5}=\frac{0+16\sqrt{5}}{10}
=\frac{16\sqrt{5}}{10}
=\frac{8\sqrt{5}}{5}
$