10x-10/2x=0

Solution for 10x-10/2x=0 equation:

10x-10/2x=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


10x*2x-10=0

Wy multiply elements

20x^2-10=0

a = 20; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·20·(-10)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*20}=\frac{0-20\sqrt{2}}{40}
=-\frac{20\sqrt{2}}{40}
=-\frac{\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*20}=\frac{0+20\sqrt{2}}{40}
=\frac{20\sqrt{2}}{40}
=\frac{\sqrt{2}}{2}
$