4k^2+6k-3+5k^2+2=0

Solution for 4k^2+6k-3+5k^2+2=0 equation:

4k^2+6k-3+5k^2+2=0

We add all the numbers together, and all the variables

9k^2+6k-1=0

a = 9; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·9·(-1)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{2}}{2*9}=\frac{-6-6\sqrt{2}}{18}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{2}}{2*9}=\frac{-6+6\sqrt{2}}{18}
$