X2-18x=-77

Solution for X2-18x=-77 equation:

X2-18X=-77

We move all terms to the left:

X2-18X-(-77)=0

We add all the numbers together, and all the variables

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
$