w^2+8w=18

Solution for w^2+8w=18 equation:

w^2+8w=18

We move all terms to the left:

w^2+8w-(18)=0

a = 1; b = 8; c = -18;
Δ = b2-4ac
Δ = 82-4·1·(-18)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{34}}{2*1}=\frac{-8-2\sqrt{34}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{34}}{2*1}=\frac{-8+2\sqrt{34}}{2}
$