12k^2-455=-7+5k^2

Solution for 12k^2-455=-7+5k^2 equation:

12k^2-455=-7+5k^2

We move all terms to the left:

12k^2-455-(-7+5k^2)=0

We get rid of parentheses

12k^2-5k^2+7-455=0

We add all the numbers together, and all the variables

7k^2-448=0

a = 7; b = 0; c = -448;
Δ = b2-4ac
Δ = 02-4·7·(-448)
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-112}{2*7}=\frac{-112}{14}
=-8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+112}{2*7}=\frac{112}{14}
=8
$