3x(x-2)=20-x

Solution for 3x(x-2)=20-x equation:

3x(x-2)=20-x

We move all terms to the left:

3x(x-2)-(20-x)=0

We add all the numbers together, and all the variables

3x(x-2)-(-1x+20)=0

We multiply parentheses

3x^2-6x-(-1x+20)=0

We get rid of parentheses

3x^2-6x+1x-20=0

We add all the numbers together, and all the variables

3x^2-5x-20=0

a = 3; b = -5; c = -20;
Δ = b2-4ac
Δ = -52-4·3·(-20)
Δ = 265
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{-(-5)-\sqrt{265}}{2*3}=\frac{5-\sqrt{265}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{265}}{2*3}=\frac{5+\sqrt{265}}{6}
$