5x-8/2x=1

Solution for 5x-8/2x=1 equation:

5x-8/2x=1

We move all terms to the left:

5x-8/2x-(1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


5x*2x-1*2x-8=0

Wy multiply elements

10x^2-2x-8=0

a = 10; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·10·(-8)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-18}{2*10}=\frac{-16}{20}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+18}{2*10}=\frac{20}{20}
=1
$