H(x)=x2+6x-27

Solution for H(x)=x2+6x-27 equation:

(H)=H2+6H-27

We move all terms to the left:

(H)-(H2+6H-27)=0

We add all the numbers together, and all the variables

-(+H^2+6H-27)+H=0

We get rid of parentheses

-H^2-6H+H+27=0

We add all the numbers together, and all the variables

-1H^2-5H+27=0

a = -1; b = -5; c = +27;
Δ = b2-4ac
Δ = -52-4·(-1)·27
Δ = 133
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{133}}{2*-1}=\frac{5-\sqrt{133}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{133}}{2*-1}=\frac{5+\sqrt{133}}{-2}
$