30x-6x^2=12

Solution for 30x-6x^2=12 equation:

30x-6x^2=12

We move all terms to the left:

30x-6x^2-(12)=0

a = -6; b = 30; c = -12;
Δ = b2-4ac
Δ = 302-4·(-6)·(-12)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{17}}{2*-6}=\frac{-30-6\sqrt{17}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{17}}{2*-6}=\frac{-30+6\sqrt{17}}{-12}
$