3x(5x+-6)=12

Solution for 3x(5x+-6)=12 equation:

3x(5x+-6)=12

We move all terms to the left:

3x(5x+-6)-(12)=0

We add all the numbers together, and all the variables

3x(5x-6)-12=0

We multiply parentheses

15x^2-18x-12=0

a = 15; b = -18; c = -12;
Δ = b2-4ac
Δ = -182-4·15·(-12)
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{29}}{2*15}=\frac{18-6\sqrt{29}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{29}}{2*15}=\frac{18+6\sqrt{29}}{30}
$