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)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-3x^2+78x=0

a = -3; b = 78; c = 0;
Δ = b2-4ac
Δ = 782-4·(-3)·0
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-78}{2*-3}=\frac{-156}{-6}
=+26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+78}{2*-3}=\frac{0}{-6}
=0
$