8x-3/5x=1

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

8x-3/5x=1

We move all terms to the left:

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

Wy multiply elements

40x^2-5x-3=0

a = 40; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·40·(-3)
Δ = 505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{505}}{2*40}=\frac{5-\sqrt{505}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{505}}{2*40}=\frac{5+\sqrt{505}}{80}
$