5/9x+4=3/8x+12

Solution for 5/9x+4=3/8x+12 equation:

5/9x+4=3/8x+12

We move all terms to the left:

5/9x+4-(3/8x+12)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



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

x∈R


We get rid of parentheses

5/9x-3/8x-12+4=0

We calculate fractions


40x/72x^2+(-27x)/72x^2-12+4=0

We add all the numbers together, and all the variables

40x/72x^2+(-27x)/72x^2-8=0

We multiply all the terms by the denominator


40x+(-27x)-8*72x^2=0

Wy multiply elements

-576x^2+40x+(-27x)=0

We get rid of parentheses

-576x^2+40x-27x=0

We add all the numbers together, and all the variables

-576x^2+13x=0

a = -576; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-576)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-576}=\frac{-26}{-1152}
=13/576
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-576}=\frac{0}{-1152}
=0
$