3=x(7-3x)+3

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

3=x(7-3x)+3

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(x(-3x+7)+3), so:

x(-3x+7)+3

We multiply parentheses

-3x^2+7x+3

Back to the equation:

-(-3x^2+7x+3)


We get rid of parentheses

3x^2-7x-3+3=0

We add all the numbers together, and all the variables

3x^2-7x=0

a = 3; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·3·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*3}=\frac{14}{6}
=2+1/3
$