15/x-1=90/5x-8

Solution for 15/x-1=90/5x-8 equation:

15/x-1=90/5x-8

We move all terms to the left:

15/x-1-(90/5x-8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x-8)!=0

x∈R


We get rid of parentheses

15/x-90/5x+8-1=0

We calculate fractions


75x/5x^2+(-90x)/5x^2+8-1=0

We add all the numbers together, and all the variables

75x/5x^2+(-90x)/5x^2+7=0

We multiply all the terms by the denominator


75x+(-90x)+7*5x^2=0

Wy multiply elements

35x^2+75x+(-90x)=0

We get rid of parentheses

35x^2+75x-90x=0

We add all the numbers together, and all the variables

35x^2-15x=0

a = 35; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·35·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*35}=\frac{0}{70}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*35}=\frac{30}{70}
=3/7
$