6=x(5-x)

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Solution for 6=x(5-x) equation: 



6=x(5-x)

We move all terms to the left:

6-(x(5-x))=0

We add all the numbers together, and all the variables

-(x(-1x+5))+6=0



We calculate terms in parentheses: -(x(-1x+5)), so:

x(-1x+5)

We multiply parentheses

-1x^2+5x

Back to the equation:

-(-1x^2+5x)



We get rid of parentheses

1x^2-5x+6=0

We add all the numbers together, and all the variables

x^2-5x+6=0

a = 1; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·1·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$


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


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*1}=\frac{6}{2}
=3
$

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