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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


10x/15x^2+12x/15x^2-3=0

We multiply all the terms by the denominator


10x+12x-3*15x^2=0

We add all the numbers together, and all the variables

22x-3*15x^2=0

Wy multiply elements

-45x^2+22x=0

a = -45; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-45)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-45}=\frac{-44}{-90}
=22/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-45}=\frac{0}{-90}
=0
$