5x-4=(1/5)(5+20x)

Solution for 5x-4=(1/5)(5+20x) equation:

5x-4=(1/5)(5+20x)

We move all terms to the left:

5x-4-((1/5)(5+20x))=0


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

x∈R


We add all the numbers together, and all the variables

5x-((+1/5)(20x+5))-4=0

We multiply parentheses ..

-((+20x^2+1/5*5))+5x-4=0

We multiply all the terms by the denominator


-((+20x^2+1+5x*5*5))-4*5*5))=0


We calculate terms in parentheses: -((+20x^2+1+5x*5*5)), so:

(+20x^2+1+5x*5*5)

We get rid of parentheses

20x^2+5x*5*5+1

Wy multiply elements

20x^2+125x*5+1

Wy multiply elements

20x^2+625x+1

Back to the equation:

-(20x^2+625x+1)


We add all the numbers together, and all the variables

-(20x^2+625x+1)=0

We get rid of parentheses

-20x^2-625x-1=0

a = -20; b = -625; c = -1;
Δ = b2-4ac
Δ = -6252-4·(-20)·(-1)
Δ = 390545
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-625)-\sqrt{390545}}{2*-20}=\frac{625-\sqrt{390545}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-625)+\sqrt{390545}}{2*-20}=\frac{625+\sqrt{390545}}{-40}
$