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^2-70x-5=0

a = -2; b = -70; c = -5;
Δ = b2-4ac
Δ = -702-4·(-2)·(-5)
Δ = 4860
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:

$\sqrt{\Delta}=\sqrt{4860}=\sqrt{324*15}=\sqrt{324}*\sqrt{15}=18\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-18\sqrt{15}}{2*-2}=\frac{70-18\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+18\sqrt{15}}{2*-2}=\frac{70+18\sqrt{15}}{-4}
$