108(6X2-6)=108(3x+3)

Solution for 108(6X2-6)=108(3x+3) equation:

108(6X^2-6)=108(3X+3)

We move all terms to the left:

108(6X^2-6)-(108(3X+3))=0

We multiply parentheses

648X^2-(108(3X+3))-648=0


We calculate terms in parentheses: -(108(3X+3)), so:

108(3X+3)

We multiply parentheses

324X+324

Back to the equation:

-(324X+324)


We get rid of parentheses

648X^2-324X-324-648=0

We add all the numbers together, and all the variables

648X^2-324X-972=0

a = 648; b = -324; c = -972;
Δ = b2-4ac
Δ = -3242-4·648·(-972)
Δ = 2624400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2624400}=1620$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-1620}{2*648}=\frac{-1296}{1296}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+1620}{2*648}=\frac{1944}{1296}
=1+1/2
$