0=45x^2-492x-2466

Solution for 0=45x^2-492x-2466 equation:

0=45x^2-492x-2466

We move all terms to the left:

0-(45x^2-492x-2466)=0

We add all the numbers together, and all the variables

-(45x^2-492x-2466)=0

We get rid of parentheses

-45x^2+492x+2466=0

a = -45; b = 492; c = +2466;
Δ = b2-4ac
Δ = 4922-4·(-45)·2466
Δ = 685944
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:

$\sqrt{\Delta}=\sqrt{685944}=\sqrt{36*19054}=\sqrt{36}*\sqrt{19054}=6\sqrt{19054}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(492)-6\sqrt{19054}}{2*-45}=\frac{-492-6\sqrt{19054}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(492)+6\sqrt{19054}}{2*-45}=\frac{-492+6\sqrt{19054}}{-90}
$