3x(x-3)=21-x

Solution for 3x(x-3)=21-x equation:

3x(x-3)=21-x

We move all terms to the left:

3x(x-3)-(21-x)=0

We add all the numbers together, and all the variables

3x(x-3)-(-1x+21)=0

We multiply parentheses

3x^2-9x-(-1x+21)=0

We get rid of parentheses

3x^2-9x+1x-21=0

We add all the numbers together, and all the variables

3x^2-8x-21=0

a = 3; b = -8; c = -21;
Δ = b2-4ac
Δ = -82-4·3·(-21)
Δ = 316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{79}}{2*3}=\frac{8-2\sqrt{79}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{79}}{2*3}=\frac{8+2\sqrt{79}}{6}
$