11-5/2x=x-46

Solution for 11-5/2x=x-46 equation:

11-5/2x=x-46

We move all terms to the left:

11-5/2x-(x-46)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-5/2x-x+46+11=0

We multiply all the terms by the denominator


-x*2x+46*2x+11*2x-5=0

Wy multiply elements

-2x^2+92x+22x-5=0

We add all the numbers together, and all the variables

-2x^2+114x-5=0

a = -2; b = 114; c = -5;
Δ = b2-4ac
Δ = 1142-4·(-2)·(-5)
Δ = 12956
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:

$\sqrt{\Delta}=\sqrt{12956}=\sqrt{4*3239}=\sqrt{4}*\sqrt{3239}=2\sqrt{3239}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-2\sqrt{3239}}{2*-2}=\frac{-114-2\sqrt{3239}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+2\sqrt{3239}}{2*-2}=\frac{-114+2\sqrt{3239}}{-4}
$