420=3x^2+5

Solution for 420=3x^2+5 equation:

420=3x^2+5

We move all terms to the left:

420-(3x^2+5)=0

We get rid of parentheses

-3x^2-5+420=0

We add all the numbers together, and all the variables

-3x^2+415=0

a = -3; b = 0; c = +415;
Δ = b2-4ac
Δ = 02-4·(-3)·415
Δ = 4980
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:

$\sqrt{\Delta}=\sqrt{4980}=\sqrt{4*1245}=\sqrt{4}*\sqrt{1245}=2\sqrt{1245}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1245}}{2*-3}=\frac{0-2\sqrt{1245}}{-6}
=-\frac{2\sqrt{1245}}{-6}
=-\frac{\sqrt{1245}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1245}}{2*-3}=\frac{0+2\sqrt{1245}}{-6}
=\frac{2\sqrt{1245}}{-6}
=\frac{\sqrt{1245}}{-3}
$