4k^2-12k=112

Solution for 4k^2-12k=112 equation:

4k^2-12k=112

We move all terms to the left:

4k^2-12k-(112)=0

a = 4; b = -12; c = -112;
Δ = b2-4ac
Δ = -122-4·4·(-112)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-44}{2*4}=\frac{-32}{8}
=-4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+44}{2*4}=\frac{56}{8}
=7
$