4x=x(35-x)

Solution for 4x=x(35-x) equation:

4x=x(35-x)

We move all terms to the left:

4x-(x(35-x))=0

We add all the numbers together, and all the variables

4x-(x(-1x+35))=0


We calculate terms in parentheses: -(x(-1x+35)), so:

x(-1x+35)

We multiply parentheses

-1x^2+35x

Back to the equation:

-(-1x^2+35x)


We get rid of parentheses

1x^2-35x+4x=0

We add all the numbers together, and all the variables

x^2-31x=0

a = 1; b = -31; c = 0;
Δ = b2-4ac
Δ = -312-4·1·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-31}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+31}{2*1}=\frac{62}{2}
=31
$