.8x^2+8x=100

Solution for .8x^2+8x=100 equation:

.8x^2+8x=100

We move all terms to the left:

.8x^2+8x-(100)=0

a = .8; b = 8; c = -100;
Δ = b2-4ac
Δ = 82-4·.8·(-100)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{6}}{2*.8}=\frac{-8-8\sqrt{6}}{1.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{6}}{2*.8}=\frac{-8+8\sqrt{6}}{1.6}
$