4k2-72=-12k

Solution for 4k2-72=-12k equation:

4k^2-72=-12k

We move all terms to the left:

4k^2-72-(-12k)=0

We get rid of parentheses

4k^2+12k-72=0

a = 4; b = 12; c = -72;
Δ = b2-4ac
Δ = 122-4·4·(-72)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-36}{2*4}=\frac{-48}{8}
=-6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+36}{2*4}=\frac{24}{8}
=3
$