100/q+10+q=10+2q

Solution for 100/q+10+q=10+2q equation:

100/q+10+q=10+2q

We move all terms to the left:

100/q+10+q-(10+2q)=0


Domain of the equation: q!=0

q∈R


We add all the numbers together, and all the variables

100/q+q-(2q+10)+10=0

We add all the numbers together, and all the variables

q+100/q-(2q+10)+10=0

We get rid of parentheses

q+100/q-2q-10+10=0

We multiply all the terms by the denominator


q*q-2q*q-10*q+10*q+100=0

We add all the numbers together, and all the variables

q*q-2q*q+100=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-1q^2+100=0

a = -1; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-1)·100
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*-1}=\frac{-20}{-2}
=+10
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*-1}=\frac{20}{-2}
=-10
$