6/q+5=4q

Solution for 6/q+5=4q equation:

6/q+5=4q

We move all terms to the left:

6/q+5-(4q)=0


Domain of the equation: q!=0

q∈R


We add all the numbers together, and all the variables

-4q+6/q+5=0

We multiply all the terms by the denominator


-4q*q+5*q+6=0

We add all the numbers together, and all the variables

5q-4q*q+6=0

Wy multiply elements

-4q^2+5q+6=0

a = -4; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-4)·6
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*-4}=\frac{-16}{-8}
=+2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*-4}=\frac{6}{-8}
=-3/4
$