H(x)=2x^2-7x-30

Solution for H(x)=2x^2-7x-30 equation:

(H)=2H^2-7H-30

We move all terms to the left:

(H)-(2H^2-7H-30)=0

We get rid of parentheses

-2H^2+H+7H+30=0

We add all the numbers together, and all the variables

-2H^2+8H+30=0

a = -2; b = 8; c = +30;
Δ = b2-4ac
Δ = 82-4·(-2)·30
Δ = 304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{19}}{2*-2}=\frac{-8-4\sqrt{19}}{-4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{19}}{2*-2}=\frac{-8+4\sqrt{19}}{-4}
$