0=3x^2-48x+86

Solution for 0=3x^2-48x+86 equation:

0=3x^2-48x+86

We move all terms to the left:

0-(3x^2-48x+86)=0

We add all the numbers together, and all the variables

-(3x^2-48x+86)=0

We get rid of parentheses

-3x^2+48x-86=0

a = -3; b = 48; c = -86;
Δ = b2-4ac
Δ = 482-4·(-3)·(-86)
Δ = 1272
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:

$\sqrt{\Delta}=\sqrt{1272}=\sqrt{4*318}=\sqrt{4}*\sqrt{318}=2\sqrt{318}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{318}}{2*-3}=\frac{-48-2\sqrt{318}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{318}}{2*-3}=\frac{-48+2\sqrt{318}}{-6}
$