0=3x^2-21x-52

Solution for 0=3x^2-21x-52 equation:

0=3x^2-21x-52

We move all terms to the left:

0-(3x^2-21x-52)=0

We add all the numbers together, and all the variables

-(3x^2-21x-52)=0

We get rid of parentheses

-3x^2+21x+52=0

a = -3; b = 21; c = +52;
Δ = b2-4ac
Δ = 212-4·(-3)·52
Δ = 1065
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{1065}}{2*-3}=\frac{-21-\sqrt{1065}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{1065}}{2*-3}=\frac{-21+\sqrt{1065}}{-6}
$