(3h-5)(-4h-9)=0

Solution for (3h-5)(-4h-9)=0 equation:

(3h-5)(-4h-9)=0

We multiply parentheses ..

(-12h^2-27h+20h+45)=0

We get rid of parentheses

-12h^2-27h+20h+45=0

We add all the numbers together, and all the variables

-12h^2-7h+45=0

a = -12; b = -7; c = +45;
Δ = b2-4ac
Δ = -72-4·(-12)·45
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-47}{2*-12}=\frac{-40}{-24}
=1+2/3
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+47}{2*-12}=\frac{54}{-24}
=-2+1/4
$