(X-2)*(3x-1)=21

Solution for (X-2)*(3x-1)=21 equation:

(X-2)(3X-1)=21

We move all terms to the left:

(X-2)(3X-1)-(21)=0

We multiply parentheses ..

(+3X^2-1X-6X+2)-21=0

We get rid of parentheses

3X^2-1X-6X+2-21=0

We add all the numbers together, and all the variables

3X^2-7X-19=0

a = 3; b = -7; c = -19;
Δ = b2-4ac
Δ = -72-4·3·(-19)
Δ = 277
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{-(-7)-\sqrt{277}}{2*3}=\frac{7-\sqrt{277}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{277}}{2*3}=\frac{7+\sqrt{277}}{6}
$