4(5x+1)=(1/2)(20x+16)+16

Solution for 4(5x+1)=(1/2)(20x+16)+16 equation:

4(5x+1)=(1/2)(20x+16)+16

We move all terms to the left:

4(5x+1)-((1/2)(20x+16)+16)=0


Domain of the equation: 2)(20x+16)+16)!=0

x∈R


We add all the numbers together, and all the variables

4(5x+1)-((+1/2)(20x+16)+16)=0

We multiply parentheses

20x-((+1/2)(20x+16)+16)+4=0

We multiply parentheses ..

-((+20x^2+1/2*16)+16)+20x+4=0

We multiply all the terms by the denominator


-((+20x^2+1+20x*2*16)+16)+4*2*16)+16)=0


We calculate terms in parentheses: -((+20x^2+1+20x*2*16)+16), so:

(+20x^2+1+20x*2*16)+16

We get rid of parentheses

20x^2+20x*2*16+1+16

We add all the numbers together, and all the variables

20x^2+20x*2*16+17

Wy multiply elements

20x^2+640x*1+17

Wy multiply elements

20x^2+640x+17

Back to the equation:

-(20x^2+640x+17)


We add all the numbers together, and all the variables

-(20x^2+640x+17)=0

We get rid of parentheses

-20x^2-640x-17=0

a = -20; b = -640; c = -17;
Δ = b2-4ac
Δ = -6402-4·(-20)·(-17)
Δ = 408240
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:

$\sqrt{\Delta}=\sqrt{408240}=\sqrt{11664*35}=\sqrt{11664}*\sqrt{35}=108\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-640)-108\sqrt{35}}{2*-20}=\frac{640-108\sqrt{35}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-640)+108\sqrt{35}}{2*-20}=\frac{640+108\sqrt{35}}{-40}
$