0=-1.5x^2+30x-54

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Solution for 0=-1.5x^2+30x-54 equation:



0=-1.5x^2+30x-54
We move all terms to the left:
0-(-1.5x^2+30x-54)=0
We add all the numbers together, and all the variables
-(-1.5x^2+30x-54)=0
We get rid of parentheses
1.5x^2-30x+54=0
a = 1.5; b = -30; c = +54;
Δ = b2-4ac
Δ = -302-4·1.5·54
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-24}{2*1.5}=\frac{6}{3} =2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+24}{2*1.5}=\frac{54}{3} =18 $

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