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(4x-3)(x=2)(x-6)=0
We move all terms to the left:
(4x-3)(x-(2)(x-6))=0
We calculate terms in parentheses: +(4x-3)(x-2(x-6)), so:We multiply parentheses ..
4x-3)(x-2(x-6)
We multiply parentheses
4x-3)(x-2x+12
We add all the numbers together, and all the variables
2x-3)(x+12
Back to the equation:
+(2x-3)(x+12)
(+2x^2+24x-3x-36)=0
We get rid of parentheses
2x^2+24x-3x-36=0
We add all the numbers together, and all the variables
2x^2+21x-36=0
a = 2; b = 21; c = -36;
Δ = b2-4ac
Δ = 212-4·2·(-36)
Δ = 729
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{729}=27$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*2}=\frac{-48}{4} =-12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*2}=\frac{6}{4} =1+1/2 $
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