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6*(2x+4)=(x-1)*(x+6)

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Solution for 6*(2x+4)=(x-1)*(x+6) equation:



6(2x+4)=(x-1)(x+6)
We move all terms to the left:
6(2x+4)-((x-1)(x+6))=0
We multiply parentheses
12x-((x-1)(x+6))+24=0
We multiply parentheses ..
-((+x^2+6x-1x-6))+12x+24=0
We calculate terms in parentheses: -((+x^2+6x-1x-6)), so:
(+x^2+6x-1x-6)
We get rid of parentheses
x^2+6x-1x-6
We add all the numbers together, and all the variables
x^2+5x-6
Back to the equation:
-(x^2+5x-6)
We add all the numbers together, and all the variables
12x-(x^2+5x-6)+24=0
We get rid of parentheses
-x^2+12x-5x+6+24=0
We add all the numbers together, and all the variables
-1x^2+7x+30=0
a = -1; b = 7; c = +30;
Δ = b2-4ac
Δ = 72-4·(-1)·30
Δ = 169
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{169}=13
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*-1}=\frac{-20}{-2} =+10
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*-1}=\frac{6}{-2} =-3

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