4x(2x-8)=5(1+2x)

Solution for 4x(2x-8)=5(1+2x) equation:

4x(2x-8)=5(1+2x)

We move all terms to the left:

4x(2x-8)-(5(1+2x))=0

We add all the numbers together, and all the variables

4x(2x-8)-(5(2x+1))=0

We multiply parentheses

8x^2-32x-(5(2x+1))=0


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

5(2x+1)

We multiply parentheses

10x+5

Back to the equation:

-(10x+5)


We get rid of parentheses

8x^2-32x-10x-5=0

We add all the numbers together, and all the variables

8x^2-42x-5=0

a = 8; b = -42; c = -5;
Δ = b2-4ac
Δ = -422-4·8·(-5)
Δ = 1924
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:

$\sqrt{\Delta}=\sqrt{1924}=\sqrt{4*481}=\sqrt{4}*\sqrt{481}=2\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{481}}{2*8}=\frac{42-2\sqrt{481}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{481}}{2*8}=\frac{42+2\sqrt{481}}{16}
$