a^2+8a=150=0

Solution for a^2+8a=150=0 equation:

a^2+8a=150=0

We move all terms to the left:

a^2+8a-(150)=0

a = 1; b = 8; c = -150;
Δ = b2-4ac
Δ = 82-4·1·(-150)
Δ = 664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{664}=\sqrt{4*166}=\sqrt{4}*\sqrt{166}=2\sqrt{166}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{166}}{2*1}=\frac{-8-2\sqrt{166}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{166}}{2*1}=\frac{-8+2\sqrt{166}}{2}
$