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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+10)!=0

x∈R


We add all the numbers together, and all the variables

1/x-(3x-4/x+10)+6=0

We get rid of parentheses

1/x-3x+4/x-10+6=0

We multiply all the terms by the denominator


-3x*x-10*x+6*x+1+4=0

We add all the numbers together, and all the variables

-4x-3x*x+5=0

Wy multiply elements

-3x^2-4x+5=0

a = -3; b = -4; c = +5;
Δ = b2-4ac
Δ = -42-4·(-3)·5
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{19}}{2*-3}=\frac{4-2\sqrt{19}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{19}}{2*-3}=\frac{4+2\sqrt{19}}{-6}
$