2/5x-8=20-3/4x

Solution for 2/5x-8=20-3/4x equation:

2/5x-8=20-3/4x

We move all terms to the left:

2/5x-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

2/5x-(-3/4x+20)-8=0

We get rid of parentheses

2/5x+3/4x-20-8=0

We calculate fractions


8x/20x^2+15x/20x^2-20-8=0

We add all the numbers together, and all the variables

8x/20x^2+15x/20x^2-28=0

We multiply all the terms by the denominator


8x+15x-28*20x^2=0

We add all the numbers together, and all the variables

23x-28*20x^2=0

Wy multiply elements

-560x^2+23x=0

a = -560; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-560)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-560}=\frac{-46}{-1120}
=23/560
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-560}=\frac{0}{-1120}
=0
$