6(x2-4)=21+6x

Solution for 6(x2-4)=21+6x equation:

6(x2-4)=21+6x

We move all terms to the left:

6(x2-4)-(21+6x)=0

We add all the numbers together, and all the variables

6(+x^2-4)-(6x+21)=0

We multiply parentheses

6x^2-(6x+21)-24=0

We get rid of parentheses

6x^2-6x-21-24=0

We add all the numbers together, and all the variables

6x^2-6x-45=0

a = 6; b = -6; c = -45;
Δ = b2-4ac
Δ = -62-4·6·(-45)
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{31}}{2*6}=\frac{6-6\sqrt{31}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{31}}{2*6}=\frac{6+6\sqrt{31}}{12}
$