0=x(3x+7)

Solution for 0=x(3x+7) equation:

0=x(3x+7)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

x(3x+7)

We multiply parentheses

3x^2+7x

Back to the equation:

-(3x^2+7x)


We get rid of parentheses

-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
$