H(x)=-x2+3

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

(H)=-H2+3

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(-1H^2+3)+H=0

We get rid of parentheses

1H^2+H-3=0

We add all the numbers together, and all the variables

H^2+H-3=0

a = 1; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·1·(-3)
Δ = 13
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{-(1)-\sqrt{13}}{2*1}=\frac{-1-\sqrt{13}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*1}=\frac{-1+\sqrt{13}}{2}
$