2/3x-3=-1/4x+21

Solution for 2/3x-3=-1/4x+21 equation:

2/3x-3=-1/4x+21

We move all terms to the left:

2/3x-3-(-1/4x+21)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+21)!=0

x∈R


We get rid of parentheses

2/3x+1/4x-21-3=0

We calculate fractions


8x/12x^2+3x/12x^2-21-3=0

We add all the numbers together, and all the variables

8x/12x^2+3x/12x^2-24=0

We multiply all the terms by the denominator


8x+3x-24*12x^2=0

We add all the numbers together, and all the variables

11x-24*12x^2=0

Wy multiply elements

-288x^2+11x=0

a = -288; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-288)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-288}=\frac{-22}{-576}
=11/288
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-288}=\frac{0}{-576}
=0
$