x^2=17x-66

Solution for x^2=17x-66 equation:

x^2=17x-66

We move all terms to the left:

x^2-(17x-66)=0

We get rid of parentheses

x^2-17x+66=0

a = 1; b = -17; c = +66;
Δ = b2-4ac
Δ = -172-4·1·66
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-5}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+5}{2*1}=\frac{22}{2}
=11
$