X2+27x-152=0

Solution for X2+27x-152=0 equation:

X2+27X-152=0

We add all the numbers together, and all the variables

X^2+27X-152=0

a = 1; b = 27; c = -152;
Δ = b2-4ac
Δ = 272-4·1·(-152)
Δ = 1337
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{1337}}{2*1}=\frac{-27-\sqrt{1337}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{1337}}{2*1}=\frac{-27+\sqrt{1337}}{2}
$