3x-11=-1/x-75

Solution for 3x-11=-1/x-75 equation:

3x-11=-1/x-75

We move all terms to the left:

3x-11-(-1/x-75)=0


Domain of the equation: x-75)!=0

x∈R


We get rid of parentheses

3x+1/x+75-11=0

We multiply all the terms by the denominator


3x*x+75*x-11*x+1=0

We add all the numbers together, and all the variables

64x+3x*x+1=0

Wy multiply elements

3x^2+64x+1=0

a = 3; b = 64; c = +1;
Δ = b2-4ac
Δ = 642-4·3·1
Δ = 4084
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:

$\sqrt{\Delta}=\sqrt{4084}=\sqrt{4*1021}=\sqrt{4}*\sqrt{1021}=2\sqrt{1021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-2\sqrt{1021}}{2*3}=\frac{-64-2\sqrt{1021}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+2\sqrt{1021}}{2*3}=\frac{-64+2\sqrt{1021}}{6}
$