X^2=5x+66

Solution for X^2=5x+66 equation:

X^2=5X+66

We move all terms to the left:

X^2-(5X+66)=0

We get rid of parentheses

X^2-5X-66=0

a = 1; b = -5; c = -66;
Δ = b2-4ac
Δ = -52-4·1·(-66)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-17}{2*1}=\frac{-12}{2}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+17}{2*1}=\frac{22}{2}
=11
$