2/3x-9=1/4x+6

Solution for 2/3x-9=1/4x+6 equation:

2/3x-9=1/4x+6

We move all terms to the left:

2/3x-9-(1/4x+6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+6)!=0

x∈R


We get rid of parentheses

2/3x-1/4x-6-9=0

We calculate fractions


8x/12x^2+(-3x)/12x^2-6-9=0

We add all the numbers together, and all the variables

8x/12x^2+(-3x)/12x^2-15=0

We multiply all the terms by the denominator


8x+(-3x)-15*12x^2=0

Wy multiply elements

-180x^2+8x+(-3x)=0

We get rid of parentheses

-180x^2+8x-3x=0

We add all the numbers together, and all the variables

-180x^2+5x=0

a = -180; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-180)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-180}=\frac{-10}{-360}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-180}=\frac{0}{-360}
=0
$