H(-3)=x2-5x-3

Solution for H(-3)=x2-5x-3 equation:

(-3)=H2-5H-3

We move all terms to the left:

(-3)-(H2-5H-3)=0

We add all the numbers together, and all the variables

-(+H^2-5H-3)+(-3)=0

We add all the numbers together, and all the variables

-(+H^2-5H-3)-3=0

We get rid of parentheses

-H^2+5H+3-3=0

We add all the numbers together, and all the variables

-1H^2+5H=0

a = -1; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-1)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-1}=\frac{-10}{-2}
=+5
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-1}=\frac{0}{-2}
=0
$