16k^2-92k+54=-6

Solution for 16k^2-92k+54=-6 equation:

16k^2-92k+54=-6

We move all terms to the left:

16k^2-92k+54-(-6)=0

We add all the numbers together, and all the variables

16k^2-92k+60=0

a = 16; b = -92; c = +60;
Δ = b2-4ac
Δ = -922-4·16·60
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-68}{2*16}=\frac{24}{32}
=3/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+68}{2*16}=\frac{160}{32}
=5
$