8x-10/5x-1=9

Solution for 8x-10/5x-1=9 equation:

8x-10/5x-1=9

We move all terms to the left:

8x-10/5x-1-(9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

8x-10/5x-10=0

We multiply all the terms by the denominator


8x*5x-10*5x-10=0

Wy multiply elements

40x^2-50x-10=0

a = 40; b = -50; c = -10;
Δ = b2-4ac
Δ = -502-4·40·(-10)
Δ = 4100
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:

$\sqrt{\Delta}=\sqrt{4100}=\sqrt{100*41}=\sqrt{100}*\sqrt{41}=10\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{41}}{2*40}=\frac{50-10\sqrt{41}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{41}}{2*40}=\frac{50+10\sqrt{41}}{80}
$