-186=6x(-2x-21)

Solution for -186=6x(-2x-21) equation:

-186=6x(-2x-21)

We move all terms to the left:

-186-(6x(-2x-21))=0


We calculate terms in parentheses: -(6x(-2x-21)), so:

6x(-2x-21)

We multiply parentheses

-12x^2-126x

Back to the equation:

-(-12x^2-126x)


We get rid of parentheses

12x^2+126x-186=0

a = 12; b = 126; c = -186;
Δ = b2-4ac
Δ = 1262-4·12·(-186)
Δ = 24804
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:

$\sqrt{\Delta}=\sqrt{24804}=\sqrt{36*689}=\sqrt{36}*\sqrt{689}=6\sqrt{689}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-6\sqrt{689}}{2*12}=\frac{-126-6\sqrt{689}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+6\sqrt{689}}{2*12}=\frac{-126+6\sqrt{689}}{24}
$