1/2x+x=1725

Solution for 1/2x+x=1725 equation:

1/2x+x=1725

We move all terms to the left:

1/2x+x-(1725)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/2x-1725=0

We multiply all the terms by the denominator


x*2x-1725*2x+1=0

Wy multiply elements

2x^2-3450x+1=0

a = 2; b = -3450; c = +1;
Δ = b2-4ac
Δ = -34502-4·2·1
Δ = 11902492
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:

$\sqrt{\Delta}=\sqrt{11902492}=\sqrt{196*60727}=\sqrt{196}*\sqrt{60727}=14\sqrt{60727}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3450)-14\sqrt{60727}}{2*2}=\frac{3450-14\sqrt{60727}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3450)+14\sqrt{60727}}{2*2}=\frac{3450+14\sqrt{60727}}{4}
$