X+3x-8=4/3x-3

Solution for X+3x-8=4/3x-3 equation:

X+3X-8=4/3X-3

We move all terms to the left:

X+3X-8-(4/3X-3)=0


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

X∈R


We add all the numbers together, and all the variables

4X-(4/3X-3)-8=0

We get rid of parentheses

4X-4/3X+3-8=0

We multiply all the terms by the denominator


4X*3X+3*3X-8*3X-4=0

Wy multiply elements

12X^2+9X-24X-4=0

We add all the numbers together, and all the variables

12X^2-15X-4=0

a = 12; b = -15; c = -4;
Δ = b2-4ac
Δ = -152-4·12·(-4)
Δ = 417
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{-(-15)-\sqrt{417}}{2*12}=\frac{15-\sqrt{417}}{24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{417}}{2*12}=\frac{15+\sqrt{417}}{24}
$