4/3x=-8/9x-400

Solution for 4/3x=-8/9x-400 equation:

4/3x=-8/9x-400

We move all terms to the left:

4/3x-(-8/9x-400)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x-400)!=0

x∈R


We get rid of parentheses

4/3x+8/9x+400=0

We calculate fractions


36x/27x^2+24x/27x^2+400=0

We multiply all the terms by the denominator


36x+24x+400*27x^2=0

We add all the numbers together, and all the variables

60x+400*27x^2=0

Wy multiply elements

10800x^2+60x=0

a = 10800; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·10800·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*10800}=\frac{-120}{21600}
=-1/180
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*10800}=\frac{0}{21600}
=0
$