2k^2+16k-45=-8

Solution for 2k^2+16k-45=-8 equation:

2k^2+16k-45=-8

We move all terms to the left:

2k^2+16k-45-(-8)=0

We add all the numbers together, and all the variables

2k^2+16k-37=0

a = 2; b = 16; c = -37;
Δ = b2-4ac
Δ = 162-4·2·(-37)
Δ = 552
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{138}}{2*2}=\frac{-16-2\sqrt{138}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{138}}{2*2}=\frac{-16+2\sqrt{138}}{4}
$