/2x+13=x-1

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

/2x+13=x-1

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

/2x-x+1+13=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-2x^2+28x=0

a = -2; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-2)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-2}=\frac{-56}{-4}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-2}=\frac{0}{-4}
=0
$