H(x)=7-3x2

Solution for H(x)=7-3x2 equation:

(H)=7-3H^2

We move all terms to the left:

(H)-(7-3H^2)=0

We get rid of parentheses

3H^2+H-7=0

a = 3; b = 1; c = -7;
Δ = b2-4ac
Δ = 12-4·3·(-7)
Δ = 85
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{85}}{2*3}=\frac{-1-\sqrt{85}}{6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{85}}{2*3}=\frac{-1+\sqrt{85}}{6}
$