1/2x+3=13x

Solution for 1/2x+3=13x equation:

1/2x+3=13x

We move all terms to the left:

1/2x+3-(13x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-13x+1/2x+3=0

We multiply all the terms by the denominator


-13x*2x+3*2x+1=0

Wy multiply elements

-26x^2+6x+1=0

a = -26; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-26)·1
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{35}}{2*-26}=\frac{-6-2\sqrt{35}}{-52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{35}}{2*-26}=\frac{-6+2\sqrt{35}}{-52}
$