80-l^2/2-392l=0

Solution for 80-l^2/2-392l=0 equation:

80-l^2/2-392l=0

We multiply all the terms by the denominator


-l^2-392l*2+80*2=0

We add all the numbers together, and all the variables

-1l^2-392l*2+160=0

Wy multiply elements

-1l^2-784l+160=0

a = -1; b = -784; c = +160;
Δ = b2-4ac
Δ = -7842-4·(-1)·160
Δ = 615296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{615296}=\sqrt{64*9614}=\sqrt{64}*\sqrt{9614}=8\sqrt{9614}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-784)-8\sqrt{9614}}{2*-1}=\frac{784-8\sqrt{9614}}{-2}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-784)+8\sqrt{9614}}{2*-1}=\frac{784+8\sqrt{9614}}{-2}
$