3x(-7x+9)=3-x

Solution for 3x(-7x+9)=3-x equation:

3x(-7x+9)=3-x

We move all terms to the left:

3x(-7x+9)-(3-x)=0

We add all the numbers together, and all the variables

3x(-7x+9)-(-1x+3)=0

We multiply parentheses

-21x^2+27x-(-1x+3)=0

We get rid of parentheses

-21x^2+27x+1x-3=0

We add all the numbers together, and all the variables

-21x^2+28x-3=0

a = -21; b = 28; c = -3;
Δ = b2-4ac
Δ = 282-4·(-21)·(-3)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{133}}{2*-21}=\frac{-28-2\sqrt{133}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{133}}{2*-21}=\frac{-28+2\sqrt{133}}{-42}
$