0=x^2+27x+74

Solution for 0=x^2+27x+74 equation:

0=x^2+27x+74

We move all terms to the left:

0-(x^2+27x+74)=0

We add all the numbers together, and all the variables

-(x^2+27x+74)=0

We get rid of parentheses

-x^2-27x-74=0

We add all the numbers together, and all the variables

-1x^2-27x-74=0

a = -1; b = -27; c = -74;
Δ = b2-4ac
Δ = -272-4·(-1)·(-74)
Δ = 433
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{433}}{2*-1}=\frac{27-\sqrt{433}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{433}}{2*-1}=\frac{27+\sqrt{433}}{-2}
$