2/9*x+13=11-3/8*x

Solution for 2/9*x+13=11-3/8*x equation:

2/9x+13=11-3/8x

We move all terms to the left:

2/9x+13-(11-3/8x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/9x-(-3/8x+11)+13=0

We get rid of parentheses

2/9x+3/8x-11+13=0

We calculate fractions


16x/72x^2+27x/72x^2-11+13=0

We add all the numbers together, and all the variables

16x/72x^2+27x/72x^2+2=0

We multiply all the terms by the denominator


16x+27x+2*72x^2=0

We add all the numbers together, and all the variables

43x+2*72x^2=0

Wy multiply elements

144x^2+43x=0

a = 144; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·144·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*144}=\frac{-86}{288}
=-43/144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*144}=\frac{0}{288}
=0
$