X(x-2)/3=5

Solution for X(x-2)/3=5 equation:

X(X-2)/3=5

We move all terms to the left:

X(X-2)/3-(5)=0

We multiply all the terms by the denominator


X(X-2)-5*3=0

We add all the numbers together, and all the variables

X(X-2)-15=0

We multiply parentheses

X^2-2X-15=0

a = 1; b = -2; c = -15;
Δ = b2-4ac
Δ = -22-4·1·(-15)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*1}=\frac{10}{2}
=5
$