3x(x-5)=12

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

3x(x-5)=12

We move all terms to the left:

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

We multiply parentheses

3x^2-15x-12=0

a = 3; b = -15; c = -12;
Δ = b2-4ac
Δ = -152-4·3·(-12)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{41}}{2*3}=\frac{15-3\sqrt{41}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{41}}{2*3}=\frac{15+3\sqrt{41}}{6}
$