19/80x+x-20=0

Solution for 19/80x+x-20=0 equation:

19/80x+x-20=0


Domain of the equation: 80x!=0

x!=0/80

x!=0

x∈R


We add all the numbers together, and all the variables

x+19/80x-20=0

We multiply all the terms by the denominator


x*80x-20*80x+19=0

Wy multiply elements

80x^2-1600x+19=0

a = 80; b = -1600; c = +19;
Δ = b2-4ac
Δ = -16002-4·80·19
Δ = 2553920
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:

$\sqrt{\Delta}=\sqrt{2553920}=\sqrt{64*39905}=\sqrt{64}*\sqrt{39905}=8\sqrt{39905}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1600)-8\sqrt{39905}}{2*80}=\frac{1600-8\sqrt{39905}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1600)+8\sqrt{39905}}{2*80}=\frac{1600+8\sqrt{39905}}{160}
$