50k^2+455k+63=7-6k^2

Solution for 50k^2+455k+63=7-6k^2 equation:

50k^2+455k+63=7-6k^2

We move all terms to the left:

50k^2+455k+63-(7-6k^2)=0

We get rid of parentheses

50k^2+6k^2+455k-7+63=0

We add all the numbers together, and all the variables

56k^2+455k+56=0

a = 56; b = 455; c = +56;
Δ = b2-4ac
Δ = 4552-4·56·56
Δ = 194481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{194481}=441$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(455)-441}{2*56}=\frac{-896}{112}
=-8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(455)+441}{2*56}=\frac{-14}{112}
=-1/8
$