0=39x^2-476x-2461

Solution for 0=39x^2-476x-2461 equation:

0=39x^2-476x-2461

We move all terms to the left:

0-(39x^2-476x-2461)=0

We add all the numbers together, and all the variables

-(39x^2-476x-2461)=0

We get rid of parentheses

-39x^2+476x+2461=0

a = -39; b = 476; c = +2461;
Δ = b2-4ac
Δ = 4762-4·(-39)·2461
Δ = 610492
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:

$\sqrt{\Delta}=\sqrt{610492}=\sqrt{4*152623}=\sqrt{4}*\sqrt{152623}=2\sqrt{152623}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(476)-2\sqrt{152623}}{2*-39}=\frac{-476-2\sqrt{152623}}{-78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(476)+2\sqrt{152623}}{2*-39}=\frac{-476+2\sqrt{152623}}{-78}
$