0=5x-10/3x-27

Solution for 0=5x-10/3x-27 equation:

0=5x-10/3x-27

We move all terms to the left:

0-(5x-10/3x-27)=0


Domain of the equation: 3x-27)!=0

x∈R


We add all the numbers together, and all the variables

-(5x-10/3x-27)=0

We get rid of parentheses

-5x+10/3x+27=0

We multiply all the terms by the denominator


-5x*3x+27*3x+10=0

Wy multiply elements

-15x^2+81x+10=0

a = -15; b = 81; c = +10;
Δ = b2-4ac
Δ = 812-4·(-15)·10
Δ = 7161
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{-(81)-\sqrt{7161}}{2*-15}=\frac{-81-\sqrt{7161}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+\sqrt{7161}}{2*-15}=\frac{-81+\sqrt{7161}}{-30}
$