0=3x^2-78x+500

Solution for 0=3x^2-78x+500 equation:

0=3x^2-78x+500

We move all terms to the left:

0-(3x^2-78x+500)=0

We add all the numbers together, and all the variables

-(3x^2-78x+500)=0

We get rid of parentheses

-3x^2+78x-500=0

a = -3; b = 78; c = -500;
Δ = b2-4ac
Δ = 782-4·(-3)·(-500)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{21}}{2*-3}=\frac{-78-2\sqrt{21}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{21}}{2*-3}=\frac{-78+2\sqrt{21}}{-6}
$