8x(x+5)=4x

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

8x(x+5)=4x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

8x^2-4x+40x=0

We add all the numbers together, and all the variables

8x^2+36x=0

a = 8; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·8·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*8}=\frac{-72}{16}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*8}=\frac{0}{16}
=0
$