5(h)=h^2-8h+12

Solution for 5(h)=h^2-8h+12 equation:

5(h)=h^2-8h+12

We move all terms to the left:

5(h)-(h^2-8h+12)=0

We get rid of parentheses

-h^2+5h+8h-12=0

We add all the numbers together, and all the variables

-1h^2+13h-12=0

a = -1; b = 13; c = -12;
Δ = b2-4ac
Δ = 132-4·(-1)·(-12)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-11}{2*-1}=\frac{-24}{-2}
=+12
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+11}{2*-1}=\frac{-2}{-2}
=1
$