3b-11=7/4b+9

Solution for 3b-11=7/4b+9 equation:

3b-11=7/4b+9

We move all terms to the left:

3b-11-(7/4b+9)=0


Domain of the equation: 4b+9)!=0

b∈R


We get rid of parentheses

3b-7/4b-9-11=0

We multiply all the terms by the denominator


3b*4b-9*4b-11*4b-7=0

Wy multiply elements

12b^2-36b-44b-7=0

We add all the numbers together, and all the variables

12b^2-80b-7=0

a = 12; b = -80; c = -7;
Δ = b2-4ac
Δ = -802-4·12·(-7)
Δ = 6736
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:

$\sqrt{\Delta}=\sqrt{6736}=\sqrt{16*421}=\sqrt{16}*\sqrt{421}=4\sqrt{421}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{421}}{2*12}=\frac{80-4\sqrt{421}}{24}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{421}}{2*12}=\frac{80+4\sqrt{421}}{24}
$