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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


8x/12x^2+9x/12x^2+5+2=0

We add all the numbers together, and all the variables

8x/12x^2+9x/12x^2+7=0

We multiply all the terms by the denominator


8x+9x+7*12x^2=0

We add all the numbers together, and all the variables

17x+7*12x^2=0

Wy multiply elements

84x^2+17x=0

a = 84; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·84·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*84}=\frac{-34}{168}
=-17/84
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*84}=\frac{0}{168}
=0
$