1/3x+9=5/8x+12

Solution for 1/3x+9=5/8x+12 equation:

1/3x+9=5/8x+12

We move all terms to the left:

1/3x+9-(5/8x+12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 8x+12)!=0

x∈R


We get rid of parentheses

1/3x-5/8x-12+9=0

We calculate fractions


8x/24x^2+(-15x)/24x^2-12+9=0

We add all the numbers together, and all the variables

8x/24x^2+(-15x)/24x^2-3=0

We multiply all the terms by the denominator


8x+(-15x)-3*24x^2=0

Wy multiply elements

-72x^2+8x+(-15x)=0

We get rid of parentheses

-72x^2+8x-15x=0

We add all the numbers together, and all the variables

-72x^2-7x=0

a = -72; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-72)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-72}=\frac{0}{-144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-72}=\frac{14}{-144}
=-7/72
$