H(x)=-2x^2-7x+4

Solution for H(x)=-2x^2-7x+4 equation:

(H)=-2H^2-7H+4

We move all terms to the left:

(H)-(-2H^2-7H+4)=0

We get rid of parentheses

2H^2+7H+H-4=0

We add all the numbers together, and all the variables

2H^2+8H-4=0

a = 2; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·2·(-4)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*2}=\frac{-8-4\sqrt{6}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*2}=\frac{-8+4\sqrt{6}}{4}
$