420=4x^2-6x+12

Solution for 420=4x^2-6x+12 equation:

420=4x^2-6x+12

We move all terms to the left:

420-(4x^2-6x+12)=0

We get rid of parentheses

-4x^2+6x-12+420=0

We add all the numbers together, and all the variables

-4x^2+6x+408=0

a = -4; b = 6; c = +408;
Δ = b2-4ac
Δ = 62-4·(-4)·408
Δ = 6564
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:

$\sqrt{\Delta}=\sqrt{6564}=\sqrt{4*1641}=\sqrt{4}*\sqrt{1641}=2\sqrt{1641}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{1641}}{2*-4}=\frac{-6-2\sqrt{1641}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{1641}}{2*-4}=\frac{-6+2\sqrt{1641}}{-8}
$