0=3x2-18x+7

Solution for 0=3x2-18x+7 equation:

0=3x^2-18x+7

We move all terms to the left:

0-(3x^2-18x+7)=0

We add all the numbers together, and all the variables

-(3x^2-18x+7)=0

We get rid of parentheses

-3x^2+18x-7=0

a = -3; b = 18; c = -7;
Δ = b2-4ac
Δ = 182-4·(-3)·(-7)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{15}}{2*-3}=\frac{-18-4\sqrt{15}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{15}}{2*-3}=\frac{-18+4\sqrt{15}}{-6}
$