-4/5x+2/3=13/4x+2

Solution for -4/5x+2/3=13/4x+2 equation:

-4/5x+2/3=13/4x+2

We move all terms to the left:

-4/5x+2/3-(13/4x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

-4/5x-13/4x-2+2/3=0

We calculate fractions


160x^2/180x^2+(-144x)/180x^2+(-585x)/180x^2-2=0

We multiply all the terms by the denominator


160x^2+(-144x)+(-585x)-2*180x^2=0

Wy multiply elements

160x^2-360x^2+(-144x)+(-585x)=0

We get rid of parentheses

160x^2-360x^2-144x-585x=0

We add all the numbers together, and all the variables

-200x^2-729x=0

a = -200; b = -729; c = 0;
Δ = b2-4ac
Δ = -7292-4·(-200)·0
Δ = 531441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{531441}=729$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-729)-729}{2*-200}=\frac{0}{-400}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-729)+729}{2*-200}=\frac{1458}{-400}
=-3+129/200
$