4k^2+9k+3=2

Solution for 4k^2+9k+3=2 equation:

4k^2+9k+3=2

We move all terms to the left:

4k^2+9k+3-(2)=0

We add all the numbers together, and all the variables

4k^2+9k+1=0

a = 4; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·4·1
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{65}}{2*4}=\frac{-9-\sqrt{65}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{65}}{2*4}=\frac{-9+\sqrt{65}}{8}
$