2(x-3)=x(13-x)

Solution for 2(x-3)=x(13-x) equation:

2(x-3)=x(13-x)

We move all terms to the left:

2(x-3)-(x(13-x))=0

We add all the numbers together, and all the variables

2(x-3)-(x(-1x+13))=0

We multiply parentheses

2x-(x(-1x+13))-6=0


We calculate terms in parentheses: -(x(-1x+13)), so:

x(-1x+13)

We multiply parentheses

-1x^2+13x

Back to the equation:

-(-1x^2+13x)


We get rid of parentheses

1x^2-13x+2x-6=0

We add all the numbers together, and all the variables

x^2-11x-6=0

a = 1; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·1·(-6)
Δ = 145
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{-(-11)-\sqrt{145}}{2*1}=\frac{11-\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{145}}{2*1}=\frac{11+\sqrt{145}}{2}
$