9/3x-12=4/5x-36

Solution for 9/3x-12=4/5x-36 equation:

9/3x-12=4/5x-36

We move all terms to the left:

9/3x-12-(4/5x-36)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x-36)!=0

x∈R


We get rid of parentheses

9/3x-4/5x+36-12=0

We calculate fractions


45x/15x^2+(-12x)/15x^2+36-12=0

We add all the numbers together, and all the variables

45x/15x^2+(-12x)/15x^2+24=0

We multiply all the terms by the denominator


45x+(-12x)+24*15x^2=0

Wy multiply elements

360x^2+45x+(-12x)=0

We get rid of parentheses

360x^2+45x-12x=0

We add all the numbers together, and all the variables

360x^2+33x=0

a = 360; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·360·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*360}=\frac{-66}{720}
=-11/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*360}=\frac{0}{720}
=0
$