7-k2=-49

Solution for 7-k2=-49 equation:

7-k2=-49

We move all terms to the left:

7-k2-(-49)=0

We add all the numbers together, and all the variables

-1k^2+56=0

a = -1; b = 0; c = +56;
Δ = b2-4ac
Δ = 02-4·(-1)·56
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*-1}=\frac{0-4\sqrt{14}}{-2}
=-\frac{4\sqrt{14}}{-2}
=-\frac{2\sqrt{14}}{-1}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*-1}=\frac{0+4\sqrt{14}}{-2}
=\frac{4\sqrt{14}}{-2}
=\frac{2\sqrt{14}}{-1}
$