5/12q+1/2q=25=-3

Solution for 5/12q+1/2q=25=-3 equation:

5/12q+1/2q=25=-3

We move all terms to the left:

5/12q+1/2q-(25)=0


Domain of the equation: 12q!=0

q!=0/12

q!=0

q∈R



Domain of the equation: 2q!=0

q!=0/2

q!=0

q∈R


We calculate fractions


10q/24q^2+12q/24q^2-25=0

We multiply all the terms by the denominator


10q+12q-25*24q^2=0

We add all the numbers together, and all the variables

22q-25*24q^2=0

Wy multiply elements

-600q^2+22q=0

a = -600; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-600)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-600}=\frac{-44}{-1200}
=11/300
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-600}=\frac{0}{-1200}
=0
$