0=36x^2-478x-2463

Solution for 0=36x^2-478x-2463 equation:

0=36x^2-478x-2463

We move all terms to the left:

0-(36x^2-478x-2463)=0

We add all the numbers together, and all the variables

-(36x^2-478x-2463)=0

We get rid of parentheses

-36x^2+478x+2463=0

a = -36; b = 478; c = +2463;
Δ = b2-4ac
Δ = 4782-4·(-36)·2463
Δ = 583156
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:

$\sqrt{\Delta}=\sqrt{583156}=\sqrt{4*145789}=\sqrt{4}*\sqrt{145789}=2\sqrt{145789}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(478)-2\sqrt{145789}}{2*-36}=\frac{-478-2\sqrt{145789}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(478)+2\sqrt{145789}}{2*-36}=\frac{-478+2\sqrt{145789}}{-72}
$