5/6x-3=5/87x

Solution for 5/6x-3=5/87x equation:

5/6x-3=5/87x

We move all terms to the left:

5/6x-3-(5/87x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 87x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-(+5/87x)-3=0

We get rid of parentheses

5/6x-5/87x-3=0

We calculate fractions


435x/522x^2+(-30x)/522x^2-3=0

We multiply all the terms by the denominator


435x+(-30x)-3*522x^2=0

Wy multiply elements

-1566x^2+435x+(-30x)=0

We get rid of parentheses

-1566x^2+435x-30x=0

We add all the numbers together, and all the variables

-1566x^2+405x=0

a = -1566; b = 405; c = 0;
Δ = b2-4ac
Δ = 4052-4·(-1566)·0
Δ = 164025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{164025}=405$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(405)-405}{2*-1566}=\frac{-810}{-3132}
=15/58
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(405)+405}{2*-1566}=\frac{0}{-3132}
=0
$