11x-4/x=10

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

11x-4/x=10

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


11x*x-10*x-4=0

We add all the numbers together, and all the variables

-10x+11x*x-4=0

Wy multiply elements

11x^2-10x-4=0

a = 11; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·11·(-4)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{69}}{2*11}=\frac{10-2\sqrt{69}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{69}}{2*11}=\frac{10+2\sqrt{69}}{22}
$