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(2x-4)(x+6)=39(24)
We move all terms to the left:
(2x-4)(x+6)-(39(24))=0
determiningTheFunctionDomain (2x-4)(x+6)-3924=0
We multiply parentheses ..
(+2x^2+12x-4x-24)-3924=0
We get rid of parentheses
2x^2+12x-4x-24-3924=0
We add all the numbers together, and all the variables
2x^2+8x-3948=0
a = 2; b = 8; c = -3948;
Δ = b2-4ac
Δ = 82-4·2·(-3948)
Δ = 31648
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{31648}=\sqrt{16*1978}=\sqrt{16}*\sqrt{1978}=4\sqrt{1978}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{1978}}{2*2}=\frac{-8-4\sqrt{1978}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{1978}}{2*2}=\frac{-8+4\sqrt{1978}}{4} $
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