1x=45+1/2x+72

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

1x=45+1/2x+72

We move all terms to the left:

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


Domain of the equation: 2x+72)!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

x-1/2x-117=0

We multiply all the terms by the denominator


x*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}
$