4/5x-2/3x=7/12

Solution for 4/5x-2/3x=7/12 equation:

4/5x-2/3x=7/12

We move all terms to the left:

4/5x-2/3x-(7/12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-2/3x-(+7/12)=0

We get rid of parentheses

4/5x-2/3x-7/12=0

We calculate fractions


(-315x^2)/180x^2+144x/180x^2+(-120x)/180x^2=0

We multiply all the terms by the denominator


(-315x^2)+144x+(-120x)=0

We get rid of parentheses

-315x^2+144x-120x=0

We add all the numbers together, and all the variables

-315x^2+24x=0

a = -315; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-315)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-315}=\frac{-48}{-630}
=8/105
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-315}=\frac{0}{-630}
=0
$