2x(x+1)=12(x+4)

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Solution for 2x(x+1)=12(x+4) equation:



2x(x+1)=12(x+4)
We move all terms to the left:
2x(x+1)-(12(x+4))=0
We multiply parentheses
2x^2+2x-(12(x+4))=0
We calculate terms in parentheses: -(12(x+4)), so:
12(x+4)
We multiply parentheses
12x+48
Back to the equation:
-(12x+48)
We get rid of parentheses
2x^2+2x-12x-48=0
We add all the numbers together, and all the variables
2x^2-10x-48=0
a = 2; b = -10; c = -48;
Δ = b2-4ac
Δ = -102-4·2·(-48)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-22}{2*2}=\frac{-12}{4} =-3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+22}{2*2}=\frac{32}{4} =8 $

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