2/3Xx-5=15-1/3x

Solution for 2/3Xx-5=15-1/3x equation:

2/3XX-5=15-1/3X

We move all terms to the left:

2/3XX-5-(15-1/3X)=0


Domain of the equation: 3XX!=0

X!=0/1

X!=0

X∈R



Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

2/3XX-(-1/3X+15)-5=0

We get rid of parentheses

2/3XX+1/3X-15-5=0

We calculate fractions


6X/9X^2+3X/9X^2-15-5=0

We add all the numbers together, and all the variables

6X/9X^2+3X/9X^2-20=0

We multiply all the terms by the denominator


6X+3X-20*9X^2=0

We add all the numbers together, and all the variables

9X-20*9X^2=0

Wy multiply elements

-180X^2+9X=0

a = -180; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-180)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-180}=\frac{-18}{-360}
=1/20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-180}=\frac{0}{-360}
=0
$