12k^2-67k+14=-41

Solution for 12k^2-67k+14=-41 equation:

12k^2-67k+14=-41

We move all terms to the left:

12k^2-67k+14-(-41)=0

We add all the numbers together, and all the variables

12k^2-67k+55=0

a = 12; b = -67; c = +55;
Δ = b2-4ac
Δ = -672-4·12·55
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-67)-43}{2*12}=\frac{24}{24}
=1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+43}{2*12}=\frac{110}{24}
=4+7/12
$