7k^2=-1+10k

Solution for 7k^2=-1+10k equation:

7k^2=-1+10k

We move all terms to the left:

7k^2-(-1+10k)=0

We add all the numbers together, and all the variables

7k^2-(10k-1)=0

We get rid of parentheses

7k^2-10k+1=0

a = 7; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·7·1
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{2}}{2*7}=\frac{10-6\sqrt{2}}{14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{2}}{2*7}=\frac{10+6\sqrt{2}}{14}
$