-7/9x-2/3=3/8x+15

Solution for -7/9x-2/3=3/8x+15 equation:

-7/9x-2/3=3/8x+15

We move all terms to the left:

-7/9x-2/3-(3/8x+15)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 8x+15)!=0

x∈R


We get rid of parentheses

-7/9x-3/8x-15-2/3=0

We calculate fractions


(-1152x^2)/648x^2+(-504x)/648x^2+(-243x)/648x^2-15=0

We multiply all the terms by the denominator


(-1152x^2)+(-504x)+(-243x)-15*648x^2=0

Wy multiply elements

(-1152x^2)-9720x^2+(-504x)+(-243x)=0

We get rid of parentheses

-1152x^2-9720x^2-504x-243x=0

We add all the numbers together, and all the variables

-10872x^2-747x=0

a = -10872; b = -747; c = 0;
Δ = b2-4ac
Δ = -7472-4·(-10872)·0
Δ = 558009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{558009}=747$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-747)-747}{2*-10872}=\frac{0}{-21744}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-747)+747}{2*-10872}=\frac{1494}{-21744}
=-83/1208
$