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8q-4q-10/q=
We move all terms to the left:
8q-4q-10/q-()=0
Domain of the equation: q!=0We add all the numbers together, and all the variables
q∈R
4q-10/q=0
We multiply all the terms by the denominator
4q*q-10=0
Wy multiply elements
4q^2-10=0
a = 4; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·4·(-10)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*4}=\frac{0-4\sqrt{10}}{8} =-\frac{4\sqrt{10}}{8} =-\frac{\sqrt{10}}{2} $$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*4}=\frac{0+4\sqrt{10}}{8} =\frac{4\sqrt{10}}{8} =\frac{\sqrt{10}}{2} $
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