-4k2-10k-3=-12-5k2

Solution for -4k2-10k-3=-12-5k2 equation:

-4k^2-10k-3=-12-5k^2

We move all terms to the left:

-4k^2-10k-3-(-12-5k^2)=0

We get rid of parentheses

-4k^2+5k^2-10k+12-3=0

We add all the numbers together, and all the variables

k^2-10k+9=0

a = 1; b = -10; c = +9;
Δ = b2-4ac
Δ = -102-4·1·9
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8}{2*1}=\frac{2}{2}
=1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8}{2*1}=\frac{18}{2}
=9
$