X*3+6x^2+9x-32=0

Solution for X*3+6x^2+9x-32=0 equation:

X*3+6X^2+9X-32=0

We add all the numbers together, and all the variables

6X^2+9X+X*3-32=0

Wy multiply elements

6X^2+9X+3X-32=0

We add all the numbers together, and all the variables

6X^2+12X-32=0

a = 6; b = 12; c = -32;
Δ = b2-4ac
Δ = 122-4·6·(-32)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{57}}{2*6}=\frac{-12-4\sqrt{57}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{57}}{2*6}=\frac{-12+4\sqrt{57}}{12}
$