8x-3x/5x=1

Solution for 8x-3x/5x=1 equation:

8x-3x/5x=1

We move all terms to the left:

8x-3x/5x-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


8x*5x-3x-1*5x=0

We add all the numbers together, and all the variables

-3x+8x*5x-1*5x=0

Wy multiply elements

40x^2-3x-5x=0

We add all the numbers together, and all the variables

40x^2-8x=0

a = 40; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·40·0
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*40}=\frac{0}{80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*40}=\frac{16}{80}
=1/5
$