8x-5/9x-5=0.8

Solution for 8x-5/9x-5=0.8 equation:

8x-5/9x-5=0.8

We move all terms to the left:

8x-5/9x-5-(0.8)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

8x-5/9x-5.8=0

We multiply all the terms by the denominator


8x*9x-(5.8)*9x-5=0

We multiply parentheses

8x*9x-52.2x-5=0

Wy multiply elements

72x^2-52.2x-5=0

a = 72; b = -52.2; c = -5;
Δ = b2-4ac
Δ = -52.22-4·72·(-5)
Δ = 4164.84
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{-(-52.2)-\sqrt{4164.84}}{2*72}=\frac{52.2-\sqrt{4164.84}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52.2)+\sqrt{4164.84}}{2*72}=\frac{52.2+\sqrt{4164.84}}{144}
$