14x-11=90/x+1

Solution for 14x-11=90/x+1 equation:

14x-11=90/x+1

We move all terms to the left:

14x-11-(90/x+1)=0


Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

14x-90/x-1-11=0

We multiply all the terms by the denominator


14x*x-1*x-11*x-90=0

We add all the numbers together, and all the variables

-12x+14x*x-90=0

Wy multiply elements

14x^2-12x-90=0

a = 14; b = -12; c = -90;
Δ = b2-4ac
Δ = -122-4·14·(-90)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-72}{2*14}=\frac{-60}{28}
=-2+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+72}{2*14}=\frac{84}{28}
=3
$