(4-x)=x(9-5x)

Solution for (4-x)=x(9-5x) equation:

(4-x)=x(9-5x)

We move all terms to the left:

(4-x)-(x(9-5x))=0

We add all the numbers together, and all the variables

(-1x+4)-(x(-5x+9))=0

We get rid of parentheses

-1x-(x(-5x+9))+4=0


We calculate terms in parentheses: -(x(-5x+9)), so:

x(-5x+9)

We multiply parentheses

-5x^2+9x

Back to the equation:

-(-5x^2+9x)


We get rid of parentheses

5x^2-9x-1x+4=0

We add all the numbers together, and all the variables

5x^2-10x+4=0

a = 5; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·5·4
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{5}}{2*5}=\frac{10-2\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{5}}{2*5}=\frac{10+2\sqrt{5}}{10}
$