3k^2-18k-57=-9

Solution for 3k^2-18k-57=-9 equation:

3k^2-18k-57=-9

We move all terms to the left:

3k^2-18k-57-(-9)=0

We add all the numbers together, and all the variables

3k^2-18k-48=0

a = 3; b = -18; c = -48;
Δ = b2-4ac
Δ = -182-4·3·(-48)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-30}{2*3}=\frac{-12}{6}
=-2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+30}{2*3}=\frac{48}{6}
=8
$