25-1/4q=5+2q

Solution for 25-1/4q=5+2q equation:

25-1/4q=5+2q

We move all terms to the left:

25-1/4q-(5+2q)=0


Domain of the equation: 4q!=0

q!=0/4

q!=0

q∈R


We add all the numbers together, and all the variables

-1/4q-(2q+5)+25=0

We get rid of parentheses

-1/4q-2q-5+25=0

We multiply all the terms by the denominator


-2q*4q-5*4q+25*4q-1=0

Wy multiply elements

-8q^2-20q+100q-1=0

We add all the numbers together, and all the variables

-8q^2+80q-1=0

a = -8; b = 80; c = -1;
Δ = b2-4ac
Δ = 802-4·(-8)·(-1)
Δ = 6368
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:

$\sqrt{\Delta}=\sqrt{6368}=\sqrt{16*398}=\sqrt{16}*\sqrt{398}=4\sqrt{398}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-4\sqrt{398}}{2*-8}=\frac{-80-4\sqrt{398}}{-16}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+4\sqrt{398}}{2*-8}=\frac{-80+4\sqrt{398}}{-16}
$