H(x)=3x2-6x-15

Solution for H(x)=3x2-6x-15 equation:

(H)=3H^2-6H-15

We move all terms to the left:

(H)-(3H^2-6H-15)=0

We get rid of parentheses

-3H^2+H+6H+15=0

We add all the numbers together, and all the variables

-3H^2+7H+15=0

a = -3; b = 7; c = +15;
Δ = b2-4ac
Δ = 72-4·(-3)·15
Δ = 229
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{-(7)-\sqrt{229}}{2*-3}=\frac{-7-\sqrt{229}}{-6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{229}}{2*-3}=\frac{-7+\sqrt{229}}{-6}
$