(X/5-2)(3x-1)=0

Solution for (X/5-2)(3x-1)=0 equation:

(X/5-2)(3X-1)=0


Domain of the equation: 5-2)(3X-1)!=0

We move all terms containing X to the left, all other terms to the right

-2)(3X-1)!=-5

X∈R


We multiply parentheses ..

(+3X^2-1X-6X+2)=0

We get rid of parentheses

3X^2-1X-6X+2=0

We add all the numbers together, and all the variables

3X^2-7X+2=0

a = 3; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·3·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*3}=\frac{2}{6}
=1/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*3}=\frac{12}{6}
=2
$