3/4q-1=q

Solution for 3/4q-1=q equation:

3/4q-1=q

We move all terms to the left:

3/4q-1-(q)=0


Domain of the equation: 4q!=0

q!=0/4

q!=0

q∈R


We add all the numbers together, and all the variables

-1q+3/4q-1=0

We multiply all the terms by the denominator


-1q*4q-1*4q+3=0

Wy multiply elements

-4q^2-4q+3=0

a = -4; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-4)·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-4}=\frac{-4}{-8}
=1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-4}=\frac{12}{-8}
=-1+1/2
$