6k^2-90=-12k

Solution for 6k^2-90=-12k equation:

6k^2-90=-12k

We move all terms to the left:

6k^2-90-(-12k)=0

We get rid of parentheses

6k^2+12k-90=0

a = 6; b = 12; c = -90;
Δ = b2-4ac
Δ = 122-4·6·(-90)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-48}{2*6}=\frac{-60}{12}
=-5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+48}{2*6}=\frac{36}{12}
=3
$