1/7*q=11

Solution for 1/7*q=11 equation:

1/7*q=11

We move all terms to the left:

1/7*q-(11)=0


Domain of the equation: 7*q!=0

q!=0/1

q!=0

q∈R


We multiply all the terms by the denominator


-11*7*q+1=0

Wy multiply elements

-77q*q+1=0

Wy multiply elements

-77q^2+1=0

a = -77; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-77)·1
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{77}}{2*-77}=\frac{0-2\sqrt{77}}{-154}
=-\frac{2\sqrt{77}}{-154}
=-\frac{\sqrt{77}}{-77}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{77}}{2*-77}=\frac{0+2\sqrt{77}}{-154}
=\frac{2\sqrt{77}}{-154}
=\frac{\sqrt{77}}{-77}
$