55-1/2x=x-3

Solution for 55-1/2x=x-3 equation:

55-1/2x=x-3

We move all terms to the left:

55-1/2x-(x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x-x+3+55=0

We multiply all the terms by the denominator


-x*2x+3*2x+55*2x-1=0

Wy multiply elements

-2x^2+6x+110x-1=0

We add all the numbers together, and all the variables

-2x^2+116x-1=0

a = -2; b = 116; c = -1;
Δ = b2-4ac
Δ = 1162-4·(-2)·(-1)
Δ = 13448
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:

$\sqrt{\Delta}=\sqrt{13448}=\sqrt{6724*2}=\sqrt{6724}*\sqrt{2}=82\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(116)-82\sqrt{2}}{2*-2}=\frac{-116-82\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(116)+82\sqrt{2}}{2*-2}=\frac{-116+82\sqrt{2}}{-4}
$