2k2-10k-120=12

Solution for 2k2-10k-120=12 equation:

2k^2-10k-120=12

We move all terms to the left:

2k^2-10k-120-(12)=0

We add all the numbers together, and all the variables

2k^2-10k-132=0

a = 2; b = -10; c = -132;
Δ = b2-4ac
Δ = -102-4·2·(-132)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-34}{2*2}=\frac{-24}{4}
=-6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+34}{2*2}=\frac{44}{4}
=11
$