20x+3/5x*8=500

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Solution for 20x+3/5x*8=500 equation: 



20x+3/5x*8=500

We move all terms to the left:

20x+3/5x*8-(500)=0



Domain of the equation: 5x*8!=0

x!=0/1

x!=0

x∈R



We multiply all the terms by the denominator


20x*5x*8-500*5x*8+3=0

Wy multiply elements

800x^2*8-20000x*8+3=0

Wy multiply elements

6400x^2-160000x+3=0

a = 6400; b = -160000; c = +3;
Δ = b2-4ac
Δ = -1600002-4·6400·3
Δ = 25599923200
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:


$\sqrt{\Delta}=\sqrt{25599923200}=\sqrt{25600*999997}=\sqrt{25600}*\sqrt{999997}=160\sqrt{999997}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160000)-160\sqrt{999997}}{2*6400}=\frac{160000-160\sqrt{999997}}{12800}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160000)+160\sqrt{999997}}{2*6400}=\frac{160000+160\sqrt{999997}}{12800}
$

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