2b+7/2b=-11

Solution for 2b+7/2b=-11 equation:

2b+7/2b=-11

We move all terms to the left:

2b+7/2b-(-11)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

2b+7/2b+11=0

We multiply all the terms by the denominator


2b*2b+11*2b+7=0

Wy multiply elements

4b^2+22b+7=0

a = 4; b = 22; c = +7;
Δ = b2-4ac
Δ = 222-4·4·7
Δ = 372
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{93}}{2*4}=\frac{-22-2\sqrt{93}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{93}}{2*4}=\frac{-22+2\sqrt{93}}{8}
$