(4/5)(20x+5)=16x-2

Solution for (4/5)(20x+5)=16x-2 equation:

(4/5)(20x+5)=16x-2

We move all terms to the left:

(4/5)(20x+5)-(16x-2)=0


Domain of the equation: 5)(20x+5)!=0

x∈R


We add all the numbers together, and all the variables

(+4/5)(20x+5)-(16x-2)=0

We get rid of parentheses

(+4/5)(20x+5)-16x+2=0

We multiply parentheses ..

(+80x^2+4/5*5)-16x+2=0

We multiply all the terms by the denominator


(+80x^2+4-16x*5*5)+2*5*5)=0

We add all the numbers together, and all the variables

(+80x^2+4-16x*5*5)=0

We get rid of parentheses

80x^2-16x*5*5+4=0

Wy multiply elements

80x^2-400x*5+4=0

Wy multiply elements

80x^2-2000x+4=0

a = 80; b = -2000; c = +4;
Δ = b2-4ac
Δ = -20002-4·80·4
Δ = 3998720
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:

$\sqrt{\Delta}=\sqrt{3998720}=\sqrt{1024*3905}=\sqrt{1024}*\sqrt{3905}=32\sqrt{3905}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2000)-32\sqrt{3905}}{2*80}=\frac{2000-32\sqrt{3905}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2000)+32\sqrt{3905}}{2*80}=\frac{2000+32\sqrt{3905}}{160}
$