100-q=4q+10/q

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

100-q=4q+10/q

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-1q^2-4q^2+100q-10=0

We add all the numbers together, and all the variables

-5q^2+100q-10=0

a = -5; b = 100; c = -10;
Δ = b2-4ac
Δ = 1002-4·(-5)·(-10)
Δ = 9800
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:

$\sqrt{\Delta}=\sqrt{9800}=\sqrt{4900*2}=\sqrt{4900}*\sqrt{2}=70\sqrt{2}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-70\sqrt{2}}{2*-5}=\frac{-100-70\sqrt{2}}{-10}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+70\sqrt{2}}{2*-5}=\frac{-100+70\sqrt{2}}{-10}
$