1=3x-11/x-3

Solution for 1=3x-11/x-3 equation:

1=3x-11/x-3

We move all terms to the left:

1-(3x-11/x-3)=0


Domain of the equation: x-3)!=0

x∈R


We get rid of parentheses

-3x+11/x+3+1=0

We multiply all the terms by the denominator


-3x*x+3*x+1*x+11=0

We add all the numbers together, and all the variables

4x-3x*x+11=0

Wy multiply elements

-3x^2+4x+11=0

a = -3; b = 4; c = +11;
Δ = b2-4ac
Δ = 42-4·(-3)·11
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{37}}{2*-3}=\frac{-4-2\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{37}}{2*-3}=\frac{-4+2\sqrt{37}}{-6}
$