X(2)-5=(x-1)(3)+4

Solution for X(2)-5=(x-1)(3)+4 equation:

X(2)-5=(X-1)(3)+4

We move all terms to the left:

X(2)-5-((X-1)(3)+4)=0

We add all the numbers together, and all the variables

X^2-((X-1)3+4)-5=0


We calculate terms in parentheses: -((X-1)3+4), so:

(X-1)3+4

We multiply parentheses

3X-3+4

We add all the numbers together, and all the variables

3X+1

Back to the equation:

-(3X+1)


We get rid of parentheses

X^2-3X-1-5=0

We add all the numbers together, and all the variables

X^2-3X-6=0

a = 1; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·1·(-6)
Δ = 33
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{33}}{2*1}=\frac{3-\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*1}=\frac{3+\sqrt{33}}{2}
$