0=0.75x^2-24x+144

Solution for 0=0.75x^2-24x+144 equation:

0=0.75x^2-24x+144

We move all terms to the left:

0-(0.75x^2-24x+144)=0

We add all the numbers together, and all the variables

-(0.75x^2-24x+144)=0

We get rid of parentheses

-0.75x^2+24x-144=0

a = -0.75; b = 24; c = -144;
Δ = b2-4ac
Δ = 242-4·(-0.75)·(-144)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*-0.75}=\frac{-36}{-1.5}
=+24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*-0.75}=\frac{-12}{-1.5}
=+8
$