2/3x-10=1/4x-9

Solution for 2/3x-10=1/4x-9 equation:

2/3x-10=1/4x-9

We move all terms to the left:

2/3x-10-(1/4x-9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-9)!=0

x∈R


We get rid of parentheses

2/3x-1/4x+9-10=0

We calculate fractions


8x/12x^2+(-3x)/12x^2+9-10=0

We add all the numbers together, and all the variables

8x/12x^2+(-3x)/12x^2-1=0

We multiply all the terms by the denominator


8x+(-3x)-1*12x^2=0

Wy multiply elements

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

We get rid of parentheses

-12x^2+8x-3x=0

We add all the numbers together, and all the variables

-12x^2+5x=0

a = -12; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-12)·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*-12}=\frac{-10}{-24}
=5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-12}=\frac{0}{-24}
=0
$