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(2x-4)(x+2)=100
We move all terms to the left:
(2x-4)(x+2)-(100)=0
We multiply parentheses ..
(+2x^2+4x-4x-8)-100=0
We get rid of parentheses
2x^2+4x-4x-8-100=0
We add all the numbers together, and all the variables
2x^2-108=0
a = 2; b = 0; c = -108;
Δ = b2-4ac
Δ = 02-4·2·(-108)
Δ = 864
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*2}=\frac{0-12\sqrt{6}}{4} =-\frac{12\sqrt{6}}{4} =-3\sqrt{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*2}=\frac{0+12\sqrt{6}}{4} =\frac{12\sqrt{6}}{4} =3\sqrt{6} $
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