11/3x+11=4x-9

Solution for 11/3x+11=4x-9 equation:

11/3x+11=4x-9

We move all terms to the left:

11/3x+11-(4x-9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

11/3x-4x+9+11=0

We multiply all the terms by the denominator


-4x*3x+9*3x+11*3x+11=0

Wy multiply elements

-12x^2+27x+33x+11=0

We add all the numbers together, and all the variables

-12x^2+60x+11=0

a = -12; b = 60; c = +11;
Δ = b2-4ac
Δ = 602-4·(-12)·11
Δ = 4128
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:

$\sqrt{\Delta}=\sqrt{4128}=\sqrt{16*258}=\sqrt{16}*\sqrt{258}=4\sqrt{258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{258}}{2*-12}=\frac{-60-4\sqrt{258}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{258}}{2*-12}=\frac{-60+4\sqrt{258}}{-24}
$