3/5x-8=20+3/4x

Solution for 3/5x-8=20+3/4x equation:

3/5x-8=20+3/4x

We move all terms to the left:

3/5x-8-(20+3/4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(3/4x+20)-8=0

We get rid of parentheses

3/5x-3/4x-20-8=0

We calculate fractions


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

We add all the numbers together, and all the variables

12x/20x^2+(-15x)/20x^2-28=0

We multiply all the terms by the denominator


12x+(-15x)-28*20x^2=0

Wy multiply elements

-560x^2+12x+(-15x)=0

We get rid of parentheses

-560x^2+12x-15x=0

We add all the numbers together, and all the variables

-560x^2-3x=0

a = -560; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-560)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-560}=\frac{0}{-1120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-560}=\frac{6}{-1120}
=-3/560
$