3x^2-32x+60=x-2

Solution for 3x^2-32x+60=x-2 equation:

3x^2-32x+60=x-2

We move all terms to the left:

3x^2-32x+60-(x-2)=0

We get rid of parentheses

3x^2-32x-x+2+60=0

We add all the numbers together, and all the variables

3x^2-33x+62=0

a = 3; b = -33; c = +62;
Δ = b2-4ac
Δ = -332-4·3·62
Δ = 345
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{-(-33)-\sqrt{345}}{2*3}=\frac{33-\sqrt{345}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{345}}{2*3}=\frac{33+\sqrt{345}}{6}
$