1/2x+7=x+13x=

Solution for 1/2x+7=x+13x= equation:

1/2x+7=x+13x=

We move all terms to the left:

1/2x+7-(x+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

1/2x-(+14x)+7=0

We get rid of parentheses

1/2x-14x+7=0

We multiply all the terms by the denominator


-14x*2x+7*2x+1=0

Wy multiply elements

-28x^2+14x+1=0

a = -28; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·(-28)·1
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{77}}{2*-28}=\frac{-14-2\sqrt{77}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{77}}{2*-28}=\frac{-14+2\sqrt{77}}{-56}
$