(2x-11/7x)=3

Solution for (2x-11/7x)=3 equation:

(2x-11/7x)=3

We move all terms to the left:

(2x-11/7x)-(3)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2x-11/7x)-3=0

We get rid of parentheses

2x-11/7x-3=0

We multiply all the terms by the denominator


2x*7x-3*7x-11=0

Wy multiply elements

14x^2-21x-11=0

a = 14; b = -21; c = -11;
Δ = b2-4ac
Δ = -212-4·14·(-11)
Δ = 1057
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{1057}}{2*14}=\frac{21-\sqrt{1057}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{1057}}{2*14}=\frac{21+\sqrt{1057}}{28}
$