1/7q+7=12q=

Solution for 1/7q+7=12q= equation:

1/7q+7=12q=

We move all terms to the left:

1/7q+7-(12q)=0


Domain of the equation: 7q!=0

q!=0/7

q!=0

q∈R


We add all the numbers together, and all the variables

-12q+1/7q+7=0

We multiply all the terms by the denominator


-12q*7q+7*7q+1=0

Wy multiply elements

-84q^2+49q+1=0

a = -84; b = 49; c = +1;
Δ = b2-4ac
Δ = 492-4·(-84)·1
Δ = 2737
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-\sqrt{2737}}{2*-84}=\frac{-49-\sqrt{2737}}{-168}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{2737}}{2*-84}=\frac{-49+\sqrt{2737}}{-168}
$