100-q=10-4/q

Solution for 100-q=10-4/q equation:

100-q=10-4/q

We move all terms to the left:

100-q-(10-4/q)=0


Domain of the equation: q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

-q-(-4/q+10)+100=0

We add all the numbers together, and all the variables

-1q-(-4/q+10)+100=0

We get rid of parentheses

-1q+4/q-10+100=0

We multiply all the terms by the denominator


-1q*q-10*q+100*q+4=0

We add all the numbers together, and all the variables

90q-1q*q+4=0

Wy multiply elements

-1q^2+90q+4=0

a = -1; b = 90; c = +4;
Δ = b2-4ac
Δ = 902-4·(-1)·4
Δ = 8116
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:

$\sqrt{\Delta}=\sqrt{8116}=\sqrt{4*2029}=\sqrt{4}*\sqrt{2029}=2\sqrt{2029}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2029}}{2*-1}=\frac{-90-2\sqrt{2029}}{-2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2029}}{2*-1}=\frac{-90+2\sqrt{2029}}{-2}
$