q=15+1/4q

Solution for q=15+1/4q equation:

q=15+1/4q

We move all terms to the left:

q-(15+1/4q)=0


Domain of the equation: 4q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

q-(1/4q+15)=0

We get rid of parentheses

q-1/4q-15=0

We multiply all the terms by the denominator


q*4q-15*4q-1=0

Wy multiply elements

4q^2-60q-1=0

a = 4; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·4·(-1)
Δ = 3616
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:

$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{226}}{2*4}=\frac{60-4\sqrt{226}}{8}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{226}}{2*4}=\frac{60+4\sqrt{226}}{8}
$