q/8+q2=20/5

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Solution for q/8+q2=20/5 equation:



q/8+q2=20/5
We move all terms to the left:
q/8+q2-(20/5)=0
We add all the numbers together, and all the variables
q/8+q2-4=0
We add all the numbers together, and all the variables
q^2+q/8-4=0
We multiply all the terms by the denominator
q^2*8+q-4*8=0
We add all the numbers together, and all the variables
q^2*8+q-32=0
Wy multiply elements
8q^2+q-32=0
a = 8; b = 1; c = -32;
Δ = b2-4ac
Δ = 12-4·8·(-32)
Δ = 1025
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:
$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{41}}{2*8}=\frac{-1-5\sqrt{41}}{16} $
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{41}}{2*8}=\frac{-1+5\sqrt{41}}{16} $

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