8x-3/5x=2

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

8x-3/5x=2

We move all terms to the left:

8x-3/5x-(2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


8x*5x-2*5x-3=0

Wy multiply elements

40x^2-10x-3=0

a = 40; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·40·(-3)
Δ = 580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{145}}{2*40}=\frac{10-2\sqrt{145}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{145}}{2*40}=\frac{10+2\sqrt{145}}{80}
$