3x+4/x-10=11

Solution for 3x+4/x-10=11 equation:

3x+4/x-10=11

We move all terms to the left:

3x+4/x-10-(11)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+4/x-21=0

We multiply all the terms by the denominator


3x*x-21*x+4=0

We add all the numbers together, and all the variables

-21x+3x*x+4=0

Wy multiply elements

3x^2-21x+4=0

a = 3; b = -21; c = +4;
Δ = b2-4ac
Δ = -212-4·3·4
Δ = 393
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{-(-21)-\sqrt{393}}{2*3}=\frac{21-\sqrt{393}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{393}}{2*3}=\frac{21+\sqrt{393}}{6}
$