X(x-2)/3x=10

Solution for X(x-2)/3x=10 equation:

X(X-2)/3X=10

We move all terms to the left:

X(X-2)/3X-(10)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X(X-2)-10*3X=0

We multiply parentheses

X^2-2X-10*3X=0

Wy multiply elements

X^2-2X-30X=0

We add all the numbers together, and all the variables

X^2-32X=0

a = 1; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·1·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*1}=\frac{64}{2}
=32
$