10k2+9k=1

Solution for 10k2+9k=1 equation:

10k^2+9k=1

We move all terms to the left:

10k^2+9k-(1)=0

a = 10; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·10·(-1)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-11}{2*10}=\frac{-20}{20}
=-1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*10}=\frac{2}{20}
=1/10
$