93x-8)/(2x-5)=1/3

Solution for 93x-8)/(2x-5)=1/3 equation:

93x-8)/(2x-5)=1/3

We move all terms to the left:

93x-8)/(2x-5)-(1/3)=0


Domain of the equation: (2x!=0

x∈R


We add all the numbers together, and all the variables

93x-8)/(2x-5)-(+1/3)=0

We add all the numbers together, and all the variables

93x-8)/(2x+1/3)=0

We calculate fractions


93x+()/6x+(1*2x/6x=0

We multiply all the terms by the denominator


93x*6x+(1*2x+()=0


We calculate terms in parentheses: +(1*2x+(), so:

1*2x+(

We add all the numbers together, and all the variables

1*2x

Wy multiply elements

2x

Back to the equation:

+(2x)


We add all the numbers together, and all the variables

2x+93x*6x=0

Wy multiply elements

558x^2+2x=0

a = 558; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·558·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*558}=\frac{-4}{1116}
=-1/279
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*558}=\frac{0}{1116}
=0
$