H(x)=x^2-10x+3

Solution for H(x)=x^2-10x+3 equation:

(H)=H^2-10H+3

We move all terms to the left:

(H)-(H^2-10H+3)=0

We get rid of parentheses

-H^2+H+10H-3=0

We add all the numbers together, and all the variables

-1H^2+11H-3=0

a = -1; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·(-1)·(-3)
Δ = 109
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{-(11)-\sqrt{109}}{2*-1}=\frac{-11-\sqrt{109}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{109}}{2*-1}=\frac{-11+\sqrt{109}}{-2}
$