3(x2-4)-18=(x-1)2

Solution for 3(x2-4)-18=(x-1)2 equation:

3(x2-4)-18=(x-1)2

We move all terms to the left:

3(x2-4)-18-((x-1)2)=0

We add all the numbers together, and all the variables

3(+x^2-4)-((x-1)2)-18=0

We multiply parentheses

3x^2-((x-1)2)-12-18=0


We calculate terms in parentheses: -((x-1)2), so:

(x-1)2

We multiply parentheses

2x-2

Back to the equation:

-(2x-2)


We add all the numbers together, and all the variables

3x^2-(2x-2)-30=0

We get rid of parentheses

3x^2-2x+2-30=0

We add all the numbers together, and all the variables

3x^2-2x-28=0

a = 3; b = -2; c = -28;
Δ = b2-4ac
Δ = -22-4·3·(-28)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{85}}{2*3}=\frac{2-2\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{85}}{2*3}=\frac{2+2\sqrt{85}}{6}
$