3/2b-11/3b=13/7

Solution for 3/2b-11/3b=13/7 equation:

3/2b-11/3b=13/7

We move all terms to the left:

3/2b-11/3b-(13/7)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

3/2b-11/3b-(+13/7)=0

We get rid of parentheses

3/2b-11/3b-13/7=0

We calculate fractions


(-234b^2)/294b^2+441b/294b^2+(-1078b)/294b^2=0

We multiply all the terms by the denominator


(-234b^2)+441b+(-1078b)=0

We get rid of parentheses

-234b^2+441b-1078b=0

We add all the numbers together, and all the variables

-234b^2-637b=0

a = -234; b = -637; c = 0;
Δ = b2-4ac
Δ = -6372-4·(-234)·0
Δ = 405769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{405769}=637$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-637)-637}{2*-234}=\frac{0}{-468}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-637)+637}{2*-234}=\frac{1274}{-468}
=-2+13/18
$