H=-0.07875+4.0005x+-0.00635x2

Solution for H=-0.07875+4.0005x+-0.00635x2 equation:

=-0.07875+4.0005H+-0.00635H^2

We move all terms to the left:

-(-0.07875+4.0005H+-0.00635H^2)=0

We use the square of the difference formula

-(-0.07875+4.0005H-0.00635H^2)=0

We get rid of parentheses

0.00635H^2-4.0005H+0.07875=0

a = 0.00635; b = -4.0005; c = +0.07875;
Δ = b2-4ac
Δ = -4.00052-4·0.00635·0.07875
Δ = 16.002
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{-(-4.0005)-\sqrt{16.002}}{2*0.00635}=\frac{4.0005-\sqrt{16.002}}{0.0127}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.0005)+\sqrt{16.002}}{2*0.00635}=\frac{4.0005+\sqrt{16.002}}{0.0127}
$