4k^2+14k=14

Solution for 4k^2+14k=14 equation:

4k^2+14k=14

We move all terms to the left:

4k^2+14k-(14)=0

a = 4; b = 14; c = -14;
Δ = b2-4ac
Δ = 142-4·4·(-14)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{105}}{2*4}=\frac{-14-2\sqrt{105}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{105}}{2*4}=\frac{-14+2\sqrt{105}}{8}
$