5x-10/x-2=5

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

5x-10/x-2=5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-10/x-7=0

We multiply all the terms by the denominator


5x*x-7*x-10=0

We add all the numbers together, and all the variables

-7x+5x*x-10=0

Wy multiply elements

5x^2-7x-10=0

a = 5; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·5·(-10)
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{249}}{2*5}=\frac{7-\sqrt{249}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{249}}{2*5}=\frac{7+\sqrt{249}}{10}
$