45+1/2x+72=x

Solution for 45+1/2x+72=x equation:

45+1/2x+72=x

We move all terms to the left:

45+1/2x+72-(x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/2x+117=0

We multiply all the terms by the denominator


-1x*2x+117*2x+1=0

Wy multiply elements

-2x^2+234x+1=0

a = -2; b = 234; c = +1;
Δ = b2-4ac
Δ = 2342-4·(-2)·1
Δ = 54764
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:

$\sqrt{\Delta}=\sqrt{54764}=\sqrt{4*13691}=\sqrt{4}*\sqrt{13691}=2\sqrt{13691}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-2\sqrt{13691}}{2*-2}=\frac{-234-2\sqrt{13691}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+2\sqrt{13691}}{2*-2}=\frac{-234+2\sqrt{13691}}{-4}
$