3x(x-13)=-12

Solution for 3x(x-13)=-12 equation:

3x(x-13)=-12

We move all terms to the left:

3x(x-13)-(-12)=0

We add all the numbers together, and all the variables

3x(x-13)+12=0

We multiply parentheses

3x^2-39x+12=0

a = 3; b = -39; c = +12;
Δ = b2-4ac
Δ = -392-4·3·12
Δ = 1377
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:

$\sqrt{\Delta}=\sqrt{1377}=\sqrt{81*17}=\sqrt{81}*\sqrt{17}=9\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-9\sqrt{17}}{2*3}=\frac{39-9\sqrt{17}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+9\sqrt{17}}{2*3}=\frac{39+9\sqrt{17}}{6}
$