6x=10x(2x-8)

Solution for 6x=10x(2x-8) equation:

6x=10x(2x-8)

We move all terms to the left:

6x-(10x(2x-8))=0


We calculate terms in parentheses: -(10x(2x-8)), so:

10x(2x-8)

We multiply parentheses

20x^2-80x

Back to the equation:

-(20x^2-80x)


We get rid of parentheses

-20x^2+6x+80x=0

We add all the numbers together, and all the variables

-20x^2+86x=0

a = -20; b = 86; c = 0;
Δ = b2-4ac
Δ = 862-4·(-20)·0
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-86}{2*-20}=\frac{-172}{-40}
=4+3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+86}{2*-20}=\frac{0}{-40}
=0
$