X(-3x-27)=42

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Solution for X(-3x-27)=42 equation:



X(-3X-27)=42
We move all terms to the left:
X(-3X-27)-(42)=0
We multiply parentheses
-3X^2-27X-42=0
a = -3; b = -27; c = -42;
Δ = b2-4ac
Δ = -272-4·(-3)·(-42)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-15}{2*-3}=\frac{12}{-6} =-2 $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+15}{2*-3}=\frac{42}{-6} =-7 $

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