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

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

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

We move all terms to the left:

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


Domain of the equation: 5)(4x+5)!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We get rid of parentheses

4x^2-4x*5*5+1=0

Wy multiply elements

4x^2-100x*5+1=0

Wy multiply elements

4x^2-500x+1=0

a = 4; b = -500; c = +1;
Δ = b2-4ac
Δ = -5002-4·4·1
Δ = 249984
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:

$\sqrt{\Delta}=\sqrt{249984}=\sqrt{576*434}=\sqrt{576}*\sqrt{434}=24\sqrt{434}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-24\sqrt{434}}{2*4}=\frac{500-24\sqrt{434}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+24\sqrt{434}}{2*4}=\frac{500+24\sqrt{434}}{8}
$