X(x-2)-5(x-3)=12

Solution for X(x-2)-5(x-3)=12 equation:

X(X-2)-5(X-3)=12

We move all terms to the left:

X(X-2)-5(X-3)-(12)=0

We multiply parentheses

X^2-2X-5X+15-12=0

We add all the numbers together, and all the variables

X^2-7X+3=0

a = 1; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·1·3
Δ = 37
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{37}}{2*1}=\frac{7-\sqrt{37}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{37}}{2*1}=\frac{7+\sqrt{37}}{2}
$