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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


4x/6x^2+12x/6x^2-5+3=0

We add all the numbers together, and all the variables

4x/6x^2+12x/6x^2-2=0

We multiply all the terms by the denominator


4x+12x-2*6x^2=0

We add all the numbers together, and all the variables

16x-2*6x^2=0

Wy multiply elements

-12x^2+16x=0

a = -12; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-12)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-12}=\frac{-32}{-24}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-12}=\frac{0}{-24}
=0
$