-3x(x+4)-4x=2(x-3)+3

Solution for -3x(x+4)-4x=2(x-3)+3 equation:

-3x(x+4)-4x=2(x-3)+3

We move all terms to the left:

-3x(x+4)-4x-(2(x-3)+3)=0

We add all the numbers together, and all the variables

-4x-3x(x+4)-(2(x-3)+3)=0

We multiply parentheses

-3x^2-4x-12x-(2(x-3)+3)=0


We calculate terms in parentheses: -(2(x-3)+3), so:

2(x-3)+3

We multiply parentheses

2x-6+3

We add all the numbers together, and all the variables

2x-3

Back to the equation:

-(2x-3)


We add all the numbers together, and all the variables

-3x^2-16x-(2x-3)=0

We get rid of parentheses

-3x^2-16x-2x+3=0

We add all the numbers together, and all the variables

-3x^2-18x+3=0

a = -3; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·(-3)·3
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{10}}{2*-3}=\frac{18-6\sqrt{10}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{10}}{2*-3}=\frac{18+6\sqrt{10}}{-6}
$