2.5(4k+2)=12k2

Solution for 2.5(4k+2)=12k2 equation:

2.5(4k+2)=12k^2

We move all terms to the left:

2.5(4k+2)-(12k^2)=0

determiningTheFunctionDomain
-12k^2+2.5(4k+2)=0

We multiply parentheses

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

a = -12; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·(-12)·5
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{85}}{2*-12}=\frac{-10-2\sqrt{85}}{-24}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{85}}{2*-12}=\frac{-10+2\sqrt{85}}{-24}
$