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(7x-1)(8x+8)=(16x)

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Solution for (7x-1)(8x+8)=(16x) equation:



(7x-1)(8x+8)=(16x)
We move all terms to the left:
(7x-1)(8x+8)-((16x))=0
determiningTheFunctionDomain (7x-1)(8x+8)-16x=0
We add all the numbers together, and all the variables
-16x+(7x-1)(8x+8)=0
We multiply parentheses ..
(+56x^2+56x-8x-8)-16x=0
We get rid of parentheses
56x^2+56x-8x-16x-8=0
We add all the numbers together, and all the variables
56x^2+32x-8=0
a = 56; b = 32; c = -8;
Δ = b2-4ac
Δ = 322-4·56·(-8)
Δ = 2816
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{2816}=\sqrt{256*11}=\sqrt{256}*\sqrt{11}=16\sqrt{11}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-16\sqrt{11}}{2*56}=\frac{-32-16\sqrt{11}}{112}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+16\sqrt{11}}{2*56}=\frac{-32+16\sqrt{11}}{112}

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