x^2-27x+152=0

Solution for x^2-27x+152=0 equation:

x^2-27x+152=0

a = 1; b = -27; c = +152;
Δ = b2-4ac
Δ = -272-4·1·152
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-11}{2*1}=\frac{16}{2}
=8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+11}{2*1}=\frac{38}{2}
=19
$