H(x)=0.75x^2

Solution for H(x)=0.75x^2 equation:

(H)=0.75H^2

We move all terms to the left:

(H)-(0.75H^2)=0

We get rid of parentheses

-0.75H^2+H=0

a = -0.75; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-0.75)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-0.75}=\frac{-2}{-1.5}
=1+0.5/1.5
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-0.75}=\frac{0}{-1.5}
=0
$