-3x^2-6x+21=6x+8

Solution for -3x^2-6x+21=6x+8 equation:

-3x^2-6x+21=6x+8

We move all terms to the left:

-3x^2-6x+21-(6x+8)=0

We get rid of parentheses

-3x^2-6x-6x-8+21=0

We add all the numbers together, and all the variables

-3x^2-12x+13=0

a = -3; b = -12; c = +13;
Δ = b2-4ac
Δ = -122-4·(-3)·13
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-10\sqrt{3}}{2*-3}=\frac{12-10\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+10\sqrt{3}}{2*-3}=\frac{12+10\sqrt{3}}{-6}
$