x^2-27x-140=0

Solution for x^2-27x-140=0 equation:

x^2-27x-140=0

a = 1; b = -27; c = -140;
Δ = b2-4ac
Δ = -272-4·1·(-140)
Δ = 1289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{1289}}{2*1}=\frac{27-\sqrt{1289}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{1289}}{2*1}=\frac{27+\sqrt{1289}}{2}
$