5x^2-41x+66=x

Solution for 5x^2-41x+66=x equation:

5x^2-41x+66=x

We move all terms to the left:

5x^2-41x+66-(x)=0

We add all the numbers together, and all the variables

5x^2-42x+66=0

a = 5; b = -42; c = +66;
Δ = b2-4ac
Δ = -422-4·5·66
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{111}}{2*5}=\frac{42-2\sqrt{111}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{111}}{2*5}=\frac{42+2\sqrt{111}}{10}
$