H(x)=5x2-30x+30

Solution for H(x)=5x2-30x+30 equation:

(H)=5H^2-30H+30

We move all terms to the left:

(H)-(5H^2-30H+30)=0

We get rid of parentheses

-5H^2+H+30H-30=0

We add all the numbers together, and all the variables

-5H^2+31H-30=0

a = -5; b = 31; c = -30;
Δ = b2-4ac
Δ = 312-4·(-5)·(-30)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-19}{2*-5}=\frac{-50}{-10}
=+5
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+19}{2*-5}=\frac{-12}{-10}
=1+1/5
$