-3x(x+4)+15=-12

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Solution for -3x(x+4)+15=-12 equation:



-3x(x+4)+15=-12
We move all terms to the left:
-3x(x+4)+15-(-12)=0
We add all the numbers together, and all the variables
-3x(x+4)+27=0
We multiply parentheses
-3x^2-12x+27=0
a = -3; b = -12; c = +27;
Δ = b2-4ac
Δ = -122-4·(-3)·27
Δ = 468
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{13}}{2*-3}=\frac{12-6\sqrt{13}}{-6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{13}}{2*-3}=\frac{12+6\sqrt{13}}{-6} $

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