3x(x+3)-x(x-4)=0

Solution for 3x(x+3)-x(x-4)=0 equation:

3x(x+3)-x(x-4)=0

We multiply parentheses

3x^2-x^2+9x+4x=0

We add all the numbers together, and all the variables

2x^2+13x=0

a = 2; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·2·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*2}=\frac{-26}{4}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*2}=\frac{0}{4}
=0
$