1/x-5-4/x+2=x-3x-10

Solution for 1/x-5-4/x+2=x-3x-10 equation:

1/x-5-4/x+2=x-3x-10

We move all terms to the left:

1/x-5-4/x+2-(x-3x-10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1/x-4/x-(-2x-10)-5+2=0

We add all the numbers together, and all the variables

1/x-4/x-(-2x-10)-3=0

We get rid of parentheses

1/x-4/x+2x+10-3=0

We multiply all the terms by the denominator


2x*x+10*x-3*x+1-4=0

We add all the numbers together, and all the variables

7x+2x*x-3=0

Wy multiply elements

2x^2+7x-3=0

a = 2; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·2·(-3)
Δ = 73
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{73}}{2*2}=\frac{-7-\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{73}}{2*2}=\frac{-7+\sqrt{73}}{4}
$