-4/5x+8=-4/3x+24

Solution for -4/5x+8=-4/3x+24 equation:

-4/5x+8=-4/3x+24

We move all terms to the left:

-4/5x+8-(-4/3x+24)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x+24)!=0

x∈R


We get rid of parentheses

-4/5x+4/3x-24+8=0

We calculate fractions


(-12x)/15x^2+20x/15x^2-24+8=0

We add all the numbers together, and all the variables

(-12x)/15x^2+20x/15x^2-16=0

We multiply all the terms by the denominator


(-12x)+20x-16*15x^2=0

We add all the numbers together, and all the variables

20x+(-12x)-16*15x^2=0

Wy multiply elements

-240x^2+20x+(-12x)=0

We get rid of parentheses

-240x^2+20x-12x=0

We add all the numbers together, and all the variables

-240x^2+8x=0

a = -240; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-240)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-240}=\frac{-16}{-480}
=1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-240}=\frac{0}{-480}
=0
$