11-21/2x=x+46

Solution for 11-21/2x=x+46 equation:

11-21/2x=x+46

We move all terms to the left:

11-21/2x-(x+46)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-21/2x-x-46+11=0

We multiply all the terms by the denominator


-x*2x-46*2x+11*2x-21=0

Wy multiply elements

-2x^2-92x+22x-21=0

We add all the numbers together, and all the variables

-2x^2-70x-21=0

a = -2; b = -70; c = -21;
Δ = b2-4ac
Δ = -702-4·(-2)·(-21)
Δ = 4732
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:

$\sqrt{\Delta}=\sqrt{4732}=\sqrt{676*7}=\sqrt{676}*\sqrt{7}=26\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-26\sqrt{7}}{2*-2}=\frac{70-26\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+26\sqrt{7}}{2*-2}=\frac{70+26\sqrt{7}}{-4}
$