X^2+3(x-1)=9

Solution for X^2+3(x-1)=9 equation:

X^2+3(X-1)=9

We move all terms to the left:

X^2+3(X-1)-(9)=0

We multiply parentheses

X^2+3X-3-9=0

We add all the numbers together, and all the variables

X^2+3X-12=0

a = 1; b = 3; c = -12;
Δ = b2-4ac
Δ = 32-4·1·(-12)
Δ = 57
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{-(3)-\sqrt{57}}{2*1}=\frac{-3-\sqrt{57}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*1}=\frac{-3+\sqrt{57}}{2}
$