x(x-3)=-32(2x+6)

Solution for x(x-3)=-32(2x+6) equation:

x(x-3)=-32(2x+6)

We move all terms to the left:

x(x-3)-(-32(2x+6))=0

We multiply parentheses

x^2-3x-(-32(2x+6))=0


We calculate terms in parentheses: -(-32(2x+6)), so:

-32(2x+6)

We multiply parentheses

-64x-192

Back to the equation:

-(-64x-192)


We get rid of parentheses

x^2-3x+64x+192=0

We add all the numbers together, and all the variables

x^2+61x+192=0

a = 1; b = 61; c = +192;
Δ = b2-4ac
Δ = 612-4·1·192
Δ = 2953
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-\sqrt{2953}}{2*1}=\frac{-61-\sqrt{2953}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+\sqrt{2953}}{2*1}=\frac{-61+\sqrt{2953}}{2}
$