4k(k+14)=13

Solution for 4k(k+14)=13 equation:

4k(k+14)=13

We move all terms to the left:

4k(k+14)-(13)=0

We multiply parentheses

4k^2+56k-13=0

a = 4; b = 56; c = -13;
Δ = b2-4ac
Δ = 562-4·4·(-13)
Δ = 3344
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:

$\sqrt{\Delta}=\sqrt{3344}=\sqrt{16*209}=\sqrt{16}*\sqrt{209}=4\sqrt{209}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{209}}{2*4}=\frac{-56-4\sqrt{209}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{209}}{2*4}=\frac{-56+4\sqrt{209}}{8}
$