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7(x-4)2x=32
We move all terms to the left:
7(x-4)2x-(32)=0
We multiply parentheses
14x^2-56x-32=0
a = 14; b = -56; c = -32;
Δ = b2-4ac
Δ = -562-4·14·(-32)
Δ = 4928
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4928}=\sqrt{64*77}=\sqrt{64}*\sqrt{77}=8\sqrt{77}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{77}}{2*14}=\frac{56-8\sqrt{77}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{77}}{2*14}=\frac{56+8\sqrt{77}}{28} $
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