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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

X^2-1X-2X-9=0

We add all the numbers together, and all the variables

X^2-3X-9=0

a = 1; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·1·(-9)
Δ = 45
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{5}}{2*1}=\frac{3-3\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{5}}{2*1}=\frac{3+3\sqrt{5}}{2}
$