10x=4x(6-x)

Solution for 10x=4x(6-x) equation:

10x=4x(6-x)

We move all terms to the left:

10x-(4x(6-x))=0

We add all the numbers together, and all the variables

10x-(4x(-1x+6))=0


We calculate terms in parentheses: -(4x(-1x+6)), so:

4x(-1x+6)

We multiply parentheses

-4x^2+24x

Back to the equation:

-(-4x^2+24x)


We get rid of parentheses

4x^2-24x+10x=0

We add all the numbers together, and all the variables

4x^2-14x=0

a = 4; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·4·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*4}=\frac{28}{8}
=3+1/2
$