10/5x-2x=10

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

10/5x-2x=10

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+10/5x-10=0

We multiply all the terms by the denominator


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

Wy multiply elements

-10x^2-50x+10=0

a = -10; b = -50; c = +10;
Δ = b2-4ac
Δ = -502-4·(-10)·10
Δ = 2900
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:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{29}}{2*-10}=\frac{50-10\sqrt{29}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{29}}{2*-10}=\frac{50+10\sqrt{29}}{-20}
$