8x-5/5x=4

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

8x-5/5x=4

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


8x*5x-4*5x-5=0

Wy multiply elements

40x^2-20x-5=0

a = 40; b = -20; c = -5;
Δ = b2-4ac
Δ = -202-4·40·(-5)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{3}}{2*40}=\frac{20-20\sqrt{3}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{3}}{2*40}=\frac{20+20\sqrt{3}}{80}
$