13x+6=1/2x

Solution for 13x+6=1/2x equation:

13x+6=1/2x

We move all terms to the left:

13x+6-(1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

13x-(+1/2x)+6=0

We get rid of parentheses

13x-1/2x+6=0

We multiply all the terms by the denominator


13x*2x+6*2x-1=0

Wy multiply elements

26x^2+12x-1=0

a = 26; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·26·(-1)
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{62}}{2*26}=\frac{-12-2\sqrt{62}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{62}}{2*26}=\frac{-12+2\sqrt{62}}{52}
$