x^2=18x-77=0

Solution for x^2=18x-77=0 equation:

x^2=18x-77=0

We move all terms to the left:

x^2-(18x-77)=0

We get rid of parentheses

x^2-18x+77=0

a = 1; b = -18; c = +77;
Δ = b2-4ac
Δ = -182-4·1·77
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4}{2*1}=\frac{14}{2}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4}{2*1}=\frac{22}{2}
=11
$