4/3x-2=x-15

Solution for 4/3x-2=x-15 equation:

4/3x-2=x-15

We move all terms to the left:

4/3x-2-(x-15)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-x+15-2=0

We multiply all the terms by the denominator


-x*3x+15*3x-2*3x+4=0

Wy multiply elements

-3x^2+45x-6x+4=0

We add all the numbers together, and all the variables

-3x^2+39x+4=0

a = -3; b = 39; c = +4;
Δ = b2-4ac
Δ = 392-4·(-3)·4
Δ = 1569
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{-(39)-\sqrt{1569}}{2*-3}=\frac{-39-\sqrt{1569}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+\sqrt{1569}}{2*-3}=\frac{-39+\sqrt{1569}}{-6}
$