0=-3x^2+46x+12

Solution for 0=-3x^2+46x+12 equation:

0=-3x^2+46x+12

We move all terms to the left:

0-(-3x^2+46x+12)=0

We add all the numbers together, and all the variables

-(-3x^2+46x+12)=0

We get rid of parentheses

3x^2-46x-12=0

a = 3; b = -46; c = -12;
Δ = b2-4ac
Δ = -462-4·3·(-12)
Δ = 2260
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:

$\sqrt{\Delta}=\sqrt{2260}=\sqrt{4*565}=\sqrt{4}*\sqrt{565}=2\sqrt{565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{565}}{2*3}=\frac{46-2\sqrt{565}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{565}}{2*3}=\frac{46+2\sqrt{565}}{6}
$