X/3x+7-2x=13

Solution for X/3x+7-2x=13 equation:

X/3X+7-2X=13

We move all terms to the left:

X/3X+7-2X-(13)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

-2X+X/3X-6=0

We multiply all the terms by the denominator


-2X*3X+X-6*3X=0

We add all the numbers together, and all the variables

X-2X*3X-6*3X=0

Wy multiply elements

-6X^2+X-18X=0

We add all the numbers together, and all the variables

-6X^2-17X=0

a = -6; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-6)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-6}=\frac{0}{-12}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-6}=\frac{34}{-12}
=-2+5/6
$