4q=1/4q+15

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

4q=1/4q+15

We move all terms to the left:

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


Domain of the equation: 4q+15)!=0

q∈R


We get rid of parentheses

4q-1/4q-15=0

We multiply all the terms by the denominator


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

Wy multiply elements

16q^2-60q-1=0

a = 16; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·16·(-1)
Δ = 3664
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:

$\sqrt{\Delta}=\sqrt{3664}=\sqrt{16*229}=\sqrt{16}*\sqrt{229}=4\sqrt{229}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{229}}{2*16}=\frac{60-4\sqrt{229}}{32}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{229}}{2*16}=\frac{60+4\sqrt{229}}{32}
$