x^2-27x+92=0

Solution for x^2-27x+92=0 equation:

x^2-27x+92=0

a = 1; b = -27; c = +92;
Δ = b2-4ac
Δ = -272-4·1·92
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-19}{2*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+19}{2*1}=\frac{46}{2}
=23
$