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

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

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

We get rid of parentheses

3x^2-x-52=0

We add all the numbers together, and all the variables

3x^2-1x-52=0

a = 3; b = -1; c = -52;
Δ = b2-4ac
Δ = -12-4·3·(-52)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-25}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+25}{2*3}=\frac{26}{6}
=4+1/3
$