7k^2-7=48k

Solution for 7k^2-7=48k equation:

7k^2-7=48k

We move all terms to the left:

7k^2-7-(48k)=0

a = 7; b = -48; c = -7;
Δ = b2-4ac
Δ = -482-4·7·(-7)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-50}{2*7}=\frac{-2}{14}
=-1/7
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+50}{2*7}=\frac{98}{14}
=7
$