.5x(x+8)=192

Solution for .5x(x+8)=192 equation:

.5x(x+8)=192

We move all terms to the left:

.5x(x+8)-(192)=0

We multiply parentheses

x^2+8x-192=0

a = 1; b = 8; c = -192;
Δ = b2-4ac
Δ = 82-4·1·(-192)
Δ = 832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{13}}{2*1}=\frac{-8-8\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{13}}{2*1}=\frac{-8+8\sqrt{13}}{2}
$