10k^2-75k+125=3

Solution for 10k^2-75k+125=3 equation:

10k^2-75k+125=3

We move all terms to the left:

10k^2-75k+125-(3)=0

We add all the numbers together, and all the variables

10k^2-75k+122=0

a = 10; b = -75; c = +122;
Δ = b2-4ac
Δ = -752-4·10·122
Δ = 745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-\sqrt{745}}{2*10}=\frac{75-\sqrt{745}}{20}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{745}}{2*10}=\frac{75+\sqrt{745}}{20}
$