16k2+40k+25=40

Solution for 16k2+40k+25=40 equation:

16k^2+40k+25=40

We move all terms to the left:

16k^2+40k+25-(40)=0

We add all the numbers together, and all the variables

16k^2+40k-15=0

a = 16; b = 40; c = -15;
Δ = b2-4ac
Δ = 402-4·16·(-15)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-16\sqrt{10}}{2*16}=\frac{-40-16\sqrt{10}}{32}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+16\sqrt{10}}{2*16}=\frac{-40+16\sqrt{10}}{32}
$