10/2x+x=23

Solution for 10/2x+x=23 equation:

10/2x+x=23

We move all terms to the left:

10/2x+x-(23)=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+10/2x-23=0

We multiply all the terms by the denominator


x*2x-23*2x+10=0

Wy multiply elements

2x^2-46x+10=0

a = 2; b = -46; c = +10;
Δ = b2-4ac
Δ = -462-4·2·10
Δ = 2036
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:

$\sqrt{\Delta}=\sqrt{2036}=\sqrt{4*509}=\sqrt{4}*\sqrt{509}=2\sqrt{509}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{509}}{2*2}=\frac{46-2\sqrt{509}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{509}}{2*2}=\frac{46+2\sqrt{509}}{4}
$