6x^2-9=477

Solution for 6x^2-9=477 equation:

6x^2-9=477

We move all terms to the left:

6x^2-9-(477)=0

We add all the numbers together, and all the variables

6x^2-486=0

a = 6; b = 0; c = -486;
Δ = b2-4ac
Δ = 02-4·6·(-486)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-108}{2*6}=\frac{-108}{12}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+108}{2*6}=\frac{108}{12}
=9
$