11-5/2x=x+45

Solution for 11-5/2x=x+45 equation:

11-5/2x=x+45

We move all terms to the left:

11-5/2x-(x+45)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-5/2x-x-45+11=0

We multiply all the terms by the denominator


-x*2x-45*2x+11*2x-5=0

Wy multiply elements

-2x^2-90x+22x-5=0

We add all the numbers together, and all the variables

-2x^2-68x-5=0

a = -2; b = -68; c = -5;
Δ = b2-4ac
Δ = -682-4·(-2)·(-5)
Δ = 4584
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:

$\sqrt{\Delta}=\sqrt{4584}=\sqrt{4*1146}=\sqrt{4}*\sqrt{1146}=2\sqrt{1146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-2\sqrt{1146}}{2*-2}=\frac{68-2\sqrt{1146}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+2\sqrt{1146}}{2*-2}=\frac{68+2\sqrt{1146}}{-4}
$