10k^2-45k=-50

Solution for 10k^2-45k=-50 equation:

10k^2-45k=-50

We move all terms to the left:

10k^2-45k-(-50)=0

We add all the numbers together, and all the variables

10k^2-45k+50=0

a = 10; b = -45; c = +50;
Δ = b2-4ac
Δ = -452-4·10·50
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-5}{2*10}=\frac{40}{20}
=2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+5}{2*10}=\frac{50}{20}
=2+1/2
$