6k^2+13k+21=7+3k^2

Solution for 6k^2+13k+21=7+3k^2 equation:

6k^2+13k+21=7+3k^2

We move all terms to the left:

6k^2+13k+21-(7+3k^2)=0

We get rid of parentheses

6k^2-3k^2+13k-7+21=0

We add all the numbers together, and all the variables

3k^2+13k+14=0

a = 3; b = 13; c = +14;
Δ = b2-4ac
Δ = 132-4·3·14
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-1}{2*3}=\frac{-14}{6}
=-2+1/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+1}{2*3}=\frac{-12}{6}
=-2
$