(x)=3x^2-162x+82

Solution for (x)=3x^2-162x+82 equation:

(x)=3x^2-162x+82

We move all terms to the left:

(x)-(3x^2-162x+82)=0

We get rid of parentheses

-3x^2+x+162x-82=0

We add all the numbers together, and all the variables

-3x^2+163x-82=0

a = -3; b = 163; c = -82;
Δ = b2-4ac
Δ = 1632-4·(-3)·(-82)
Δ = 25585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(163)-\sqrt{25585}}{2*-3}=\frac{-163-\sqrt{25585}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(163)+\sqrt{25585}}{2*-3}=\frac{-163+\sqrt{25585}}{-6}
$