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(6-x)(6+x)-9(x-4)=(x-2)(6+x)
We move all terms to the left:
(6-x)(6+x)-9(x-4)-((x-2)(6+x))=0
We add all the numbers together, and all the variables
(-1x+6)(x+6)-9(x-4)-((x-2)(x+6))=0
We multiply parentheses
(-1x+6)(x+6)-9x-((x-2)(x+6))+36=0
We multiply parentheses ..
(-1x^2-6x+6x+36)-9x-((x-2)(x+6))+36=0
We calculate terms in parentheses: -((x-2)(x+6)), so:We get rid of parentheses
(x-2)(x+6)
We multiply parentheses ..
(+x^2+6x-2x-12)
We get rid of parentheses
x^2+6x-2x-12
We add all the numbers together, and all the variables
x^2+4x-12
Back to the equation:
-(x^2+4x-12)
-1x^2-x^2-6x+6x-9x-4x+36+12+36=0
We add all the numbers together, and all the variables
-2x^2-13x+84=0
a = -2; b = -13; c = +84;
Δ = b2-4ac
Δ = -132-4·(-2)·84
Δ = 841
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{841}=29$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-29}{2*-2}=\frac{-16}{-4} =+4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+29}{2*-2}=\frac{42}{-4} =-10+1/2 $
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