H=x2-10x+24

Solution for H=x2-10x+24 equation:

=H2-10H+24

We move all terms to the left:

-(H2-10H+24)=0

We add all the numbers together, and all the variables

-(+H^2-10H+24)=0

We get rid of parentheses

-H^2+10H-24=0

We add all the numbers together, and all the variables

-1H^2+10H-24=0

a = -1; b = 10; c = -24;
Δ = b2-4ac
Δ = 102-4·(-1)·(-24)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*-1}=\frac{-12}{-2}
=+6
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*-1}=\frac{-8}{-2}
=+4
$