4x(2x-1)+20=-8(x-8)

Solution for 4x(2x-1)+20=-8(x-8) equation:

4x(2x-1)+20=-8(x-8)

We move all terms to the left:

4x(2x-1)+20-(-8(x-8))=0

We multiply parentheses

8x^2-4x-(-8(x-8))+20=0


We calculate terms in parentheses: -(-8(x-8)), so:

-8(x-8)

We multiply parentheses

-8x+64

Back to the equation:

-(-8x+64)


We get rid of parentheses

8x^2-4x+8x-64+20=0

We add all the numbers together, and all the variables

8x^2+4x-44=0

a = 8; b = 4; c = -44;
Δ = b2-4ac
Δ = 42-4·8·(-44)
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{89}}{2*8}=\frac{-4-4\sqrt{89}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{89}}{2*8}=\frac{-4+4\sqrt{89}}{16}
$