12x(x-2)=-9(1+7x)

Solution for 12x(x-2)=-9(1+7x) equation:

12x(x-2)=-9(1+7x)

We move all terms to the left:

12x(x-2)-(-9(1+7x))=0

We add all the numbers together, and all the variables

12x(x-2)-(-9(7x+1))=0

We multiply parentheses

12x^2-24x-(-9(7x+1))=0


We calculate terms in parentheses: -(-9(7x+1)), so:

-9(7x+1)

We multiply parentheses

-63x-9

Back to the equation:

-(-63x-9)


We get rid of parentheses

12x^2-24x+63x+9=0

We add all the numbers together, and all the variables

12x^2+39x+9=0

a = 12; b = 39; c = +9;
Δ = b2-4ac
Δ = 392-4·12·9
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-33}{2*12}=\frac{-72}{24}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+33}{2*12}=\frac{-6}{24}
=-1/4
$