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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


64x/40x^2+(-25x)/40x^2+4+4=0

We add all the numbers together, and all the variables

64x/40x^2+(-25x)/40x^2+8=0

We multiply all the terms by the denominator


64x+(-25x)+8*40x^2=0

Wy multiply elements

320x^2+64x+(-25x)=0

We get rid of parentheses

320x^2+64x-25x=0

We add all the numbers together, and all the variables

320x^2+39x=0

a = 320; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·320·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*320}=\frac{-78}{640}
=-39/320
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*320}=\frac{0}{640}
=0
$