7-3k^2=-245

Solution for 7-3k^2=-245 equation:

7-3k^2=-245

We move all terms to the left:

7-3k^2-(-245)=0

We add all the numbers together, and all the variables

-3k^2+252=0

a = -3; b = 0; c = +252;
Δ = b2-4ac
Δ = 02-4·(-3)·252
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{21}}{2*-3}=\frac{0-12\sqrt{21}}{-6}
=-\frac{12\sqrt{21}}{-6}
=-\frac{2\sqrt{21}}{-1}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{21}}{2*-3}=\frac{0+12\sqrt{21}}{-6}
=\frac{12\sqrt{21}}{-6}
=\frac{2\sqrt{21}}{-1}
$