2/3x-3=-5/4x+8

Solution for 2/3x-3=-5/4x+8 equation:

2/3x-3=-5/4x+8

We move all terms to the left:

2/3x-3-(-5/4x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+8)!=0

x∈R


We get rid of parentheses

2/3x+5/4x-8-3=0

We calculate fractions


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

We add all the numbers together, and all the variables

8x/12x^2+15x/12x^2-11=0

We multiply all the terms by the denominator


8x+15x-11*12x^2=0

We add all the numbers together, and all the variables

23x-11*12x^2=0

Wy multiply elements

-132x^2+23x=0

a = -132; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-132)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-132}=\frac{-46}{-264}
=23/132
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-132}=\frac{0}{-264}
=0
$