-12x(x+4)=-3(x+6)+x-30

Solution for -12x(x+4)=-3(x+6)+x-30 equation:

-12x(x+4)=-3(x+6)+x-30

We move all terms to the left:

-12x(x+4)-(-3(x+6)+x-30)=0

We multiply parentheses

-12x^2-48x-(-3(x+6)+x-30)=0


We calculate terms in parentheses: -(-3(x+6)+x-30), so:

-3(x+6)+x-30

We add all the numbers together, and all the variables

x-3(x+6)-30

We multiply parentheses

x-3x-18-30

We add all the numbers together, and all the variables

-2x-48

Back to the equation:

-(-2x-48)


We get rid of parentheses

-12x^2-48x+2x+48=0

We add all the numbers together, and all the variables

-12x^2-46x+48=0

a = -12; b = -46; c = +48;
Δ = b2-4ac
Δ = -462-4·(-12)·48
Δ = 4420
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:

$\sqrt{\Delta}=\sqrt{4420}=\sqrt{4*1105}=\sqrt{4}*\sqrt{1105}=2\sqrt{1105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{1105}}{2*-12}=\frac{46-2\sqrt{1105}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{1105}}{2*-12}=\frac{46+2\sqrt{1105}}{-24}
$