0=-6x^2-21x-5

Solution for 0=-6x^2-21x-5 equation:

0=-6x^2-21x-5

We move all terms to the left:

0-(-6x^2-21x-5)=0

We add all the numbers together, and all the variables

-(-6x^2-21x-5)=0

We get rid of parentheses

6x^2+21x+5=0

a = 6; b = 21; c = +5;
Δ = b2-4ac
Δ = 212-4·6·5
Δ = 321
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{-(21)-\sqrt{321}}{2*6}=\frac{-21-\sqrt{321}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{321}}{2*6}=\frac{-21+\sqrt{321}}{12}
$