11/2x-14=x+13

Solution for 11/2x-14=x+13 equation:

11/2x-14=x+13

We move all terms to the left:

11/2x-14-(x+13)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

11/2x-x-13-14=0

We multiply all the terms by the denominator


-x*2x-13*2x-14*2x+11=0

Wy multiply elements

-2x^2-26x-28x+11=0

We add all the numbers together, and all the variables

-2x^2-54x+11=0

a = -2; b = -54; c = +11;
Δ = b2-4ac
Δ = -542-4·(-2)·11
Δ = 3004
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:

$\sqrt{\Delta}=\sqrt{3004}=\sqrt{4*751}=\sqrt{4}*\sqrt{751}=2\sqrt{751}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{751}}{2*-2}=\frac{54-2\sqrt{751}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{751}}{2*-2}=\frac{54+2\sqrt{751}}{-4}
$