12x^2+420=40x^2-1372

Solution for 12x^2+420=40x^2-1372 equation:

12x^2+420=40x^2-1372

We move all terms to the left:

12x^2+420-(40x^2-1372)=0

We get rid of parentheses

12x^2-40x^2+1372+420=0

We add all the numbers together, and all the variables

-28x^2+1792=0

a = -28; b = 0; c = +1792;
Δ = b2-4ac
Δ = 02-4·(-28)·1792
Δ = 200704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{200704}=448$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-448}{2*-28}=\frac{-448}{-56}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+448}{2*-28}=\frac{448}{-56}
=-8
$