-2/8x-9=4/3x-3

Solution for -2/8x-9=4/3x-3 equation:

-2/8x-9=4/3x-3

We move all terms to the left:

-2/8x-9-(4/3x-3)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

-2/8x-4/3x+3-9=0

We calculate fractions


(-6x)/24x^2+(-32x)/24x^2+3-9=0

We add all the numbers together, and all the variables

(-6x)/24x^2+(-32x)/24x^2-6=0

We multiply all the terms by the denominator


(-6x)+(-32x)-6*24x^2=0

Wy multiply elements

-144x^2+(-6x)+(-32x)=0

We get rid of parentheses

-144x^2-6x-32x=0

We add all the numbers together, and all the variables

-144x^2-38x=0

a = -144; b = -38; c = 0;
Δ = b2-4ac
Δ = -382-4·(-144)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-38}{2*-144}=\frac{0}{-288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+38}{2*-144}=\frac{76}{-288}
=-19/72
$