25+q+1/2q=3

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

25+q+1/2q=3

We move all terms to the left:

25+q+1/2q-(3)=0


Domain of the equation: 2q!=0

q!=0/2

q!=0

q∈R


We add all the numbers together, and all the variables

q+1/2q+22=0

We multiply all the terms by the denominator


q*2q+22*2q+1=0

Wy multiply elements

2q^2+44q+1=0

a = 2; b = 44; c = +1;
Δ = b2-4ac
Δ = 442-4·2·1
Δ = 1928
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:

$\sqrt{\Delta}=\sqrt{1928}=\sqrt{4*482}=\sqrt{4}*\sqrt{482}=2\sqrt{482}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-2\sqrt{482}}{2*2}=\frac{-44-2\sqrt{482}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+2\sqrt{482}}{2*2}=\frac{-44+2\sqrt{482}}{4}
$