H=-0.5X2+1.8x+1.2

Solution for H=-0.5X2+1.8x+1.2 equation:

=-0.5H^2+1.8H+1.2

We move all terms to the left:

-(-0.5H^2+1.8H+1.2)=0

We get rid of parentheses

0.5H^2-1.8H-1.2=0

a = 0.5; b = -1.8; c = -1.2;
Δ = b2-4ac
Δ = -1.82-4·0.5·(-1.2)
Δ = 5.64
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{-(-1.8)-\sqrt{5.64}}{2*0.5}=\frac{1.8-\sqrt{5.64}}{1}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.8)+\sqrt{5.64}}{2*0.5}=\frac{1.8+\sqrt{5.64}}{1}
$