3x2-72x+3=-12

Solution for 3x2-72x+3=-12 equation:

3x^2-72x+3=-12

We move all terms to the left:

3x^2-72x+3-(-12)=0

We add all the numbers together, and all the variables

3x^2-72x+15=0

a = 3; b = -72; c = +15;
Δ = b2-4ac
Δ = -722-4·3·15
Δ = 5004
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:

$\sqrt{\Delta}=\sqrt{5004}=\sqrt{36*139}=\sqrt{36}*\sqrt{139}=6\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-6\sqrt{139}}{2*3}=\frac{72-6\sqrt{139}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+6\sqrt{139}}{2*3}=\frac{72+6\sqrt{139}}{6}
$