H(x)=2x^2-20x-50

Solution for H(x)=2x^2-20x-50 equation:

(H)=2H^2-20H-50

We move all terms to the left:

(H)-(2H^2-20H-50)=0

We get rid of parentheses

-2H^2+H+20H+50=0

We add all the numbers together, and all the variables

-2H^2+21H+50=0

a = -2; b = 21; c = +50;
Δ = b2-4ac
Δ = 212-4·(-2)·50
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-29}{2*-2}=\frac{-50}{-4}
=12+1/2
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+29}{2*-2}=\frac{8}{-4}
=-2
$