x/6x-11=4x+13

Solution for x/6x-11=4x+13 equation:

x/6x-11=4x+13

We move all terms to the left:

x/6x-11-(4x+13)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

x/6x-4x-13-11=0

We multiply all the terms by the denominator


x-4x*6x-13*6x-11*6x=0

Wy multiply elements

-24x^2+x-78x-66x=0

We add all the numbers together, and all the variables

-24x^2-143x=0

a = -24; b = -143; c = 0;
Δ = b2-4ac
Δ = -1432-4·(-24)·0
Δ = 20449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20449}=143$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-143)-143}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-143)+143}{2*-24}=\frac{286}{-48}
=-5+23/24
$