5x-10=1/2x

Solution for 5x-10=1/2x equation:

5x-10=1/2x

We move all terms to the left:

5x-10-(1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+1/2x)-10=0

We get rid of parentheses

5x-1/2x-10=0

We multiply all the terms by the denominator


5x*2x-10*2x-1=0

Wy multiply elements

10x^2-20x-1=0

a = 10; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·10·(-1)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{110}}{2*10}=\frac{20-2\sqrt{110}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{110}}{2*10}=\frac{20+2\sqrt{110}}{20}
$