100+4q^/q=8q

Solution for 100+4q^/q=8q equation:

100+4q^/q=8q

We move all terms to the left:

100+4q^/q-(8q)=0


Domain of the equation: q!=0

q∈R


We add all the numbers together, and all the variables

-8q+4q^/q+100=0

We multiply all the terms by the denominator


-8q*q+4q^+100*q=0

We add all the numbers together, and all the variables

104q-8q*q=0

Wy multiply elements

-8q^2+104q=0

a = -8; b = 104; c = 0;
Δ = b2-4ac
Δ = 1042-4·(-8)·0
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-104}{2*-8}=\frac{-208}{-16}
=+13
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+104}{2*-8}=\frac{0}{-16}
=0
$