5(20x+10)=5/10x

Solution for 5(20x+10)=5/10x equation:

5(20x+10)=5/10x

We move all terms to the left:

5(20x+10)-(5/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5(20x+10)-(+5/10x)=0

We multiply parentheses

100x-(+5/10x)+50=0

We get rid of parentheses

100x-5/10x+50=0

We multiply all the terms by the denominator


100x*10x+50*10x-5=0

Wy multiply elements

1000x^2+500x-5=0

a = 1000; b = 500; c = -5;
Δ = b2-4ac
Δ = 5002-4·1000·(-5)
Δ = 270000
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:

$\sqrt{\Delta}=\sqrt{270000}=\sqrt{90000*3}=\sqrt{90000}*\sqrt{3}=300\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-300\sqrt{3}}{2*1000}=\frac{-500-300\sqrt{3}}{2000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+300\sqrt{3}}{2*1000}=\frac{-500+300\sqrt{3}}{2000}
$