-3x(x+4)+7=-9

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Solution for -3x(x+4)+7=-9 equation:



-3x(x+4)+7=-9
We move all terms to the left:
-3x(x+4)+7-(-9)=0
We add all the numbers together, and all the variables
-3x(x+4)+16=0
We multiply parentheses
-3x^2-12x+16=0
a = -3; b = -12; c = +16;
Δ = b2-4ac
Δ = -122-4·(-3)·16
Δ = 336
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:
$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{21}}{2*-3}=\frac{12-4\sqrt{21}}{-6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{21}}{2*-3}=\frac{12+4\sqrt{21}}{-6} $

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