5x-8/4x=9/3

Solution for 5x-8/4x=9/3 equation:

5x-8/4x=9/3

We move all terms to the left:

5x-8/4x-(9/3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5x-8/4x-3=0

We multiply all the terms by the denominator


5x*4x-3*4x-8=0

Wy multiply elements

20x^2-12x-8=0

a = 20; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·20·(-8)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-28}{2*20}=\frac{-16}{40}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+28}{2*20}=\frac{40}{40}
=1
$