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(2x-4)(x+6)=4x+8
We move all terms to the left:
(2x-4)(x+6)-(4x+8)=0
We get rid of parentheses
(2x-4)(x+6)-4x-8=0
We multiply parentheses ..
(+2x^2+12x-4x-24)-4x-8=0
We get rid of parentheses
2x^2+12x-4x-4x-24-8=0
We add all the numbers together, and all the variables
2x^2+4x-32=0
a = 2; b = 4; c = -32;
Δ = b2-4ac
Δ = 42-4·2·(-32)
Δ = 272
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{17}}{2*2}=\frac{-4-4\sqrt{17}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{17}}{2*2}=\frac{-4+4\sqrt{17}}{4} $
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