35=x(13.5-x)

Solution for 35=x(13.5-x) equation:

35=x(13.5-x)

We move all terms to the left:

35-(x(13.5-x))=0

We add all the numbers together, and all the variables

-(x(-1x+13.5))+35=0


We calculate terms in parentheses: -(x(-1x+13.5)), so:

x(-1x+13.5)

We multiply parentheses

-1x^2+13.5x

Back to the equation:

-(-1x^2+13.5x)


We get rid of parentheses

1x^2-13.5x+35=0

We add all the numbers together, and all the variables

x^2-13.5x+35=0

a = 1; b = -13.5; c = +35;
Δ = b2-4ac
Δ = -13.52-4·1·35
Δ = 42.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13.5)-\sqrt{42.25}}{2*1}=\frac{13.5-\sqrt{42.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13.5)+\sqrt{42.25}}{2*1}=\frac{13.5+\sqrt{42.25}}{2}
$