1/2*8b+20=1/3*18b+6

Solution for 1/2*8b+20=1/3*18b+6 equation:

1/2*8b+20=1/3*18b+6

We move all terms to the left:

1/2*8b+20-(1/3*18b+6)=0


Domain of the equation: 2*8b!=0

b!=0/1

b!=0

b∈R



Domain of the equation: 3*18b+6)!=0

b∈R


We get rid of parentheses

1/2*8b-1/3*18b-6+20=0

We calculate fractions


54b/2592b^2+(-128b)/2592b^2-6+20=0

We add all the numbers together, and all the variables

54b/2592b^2+(-128b)/2592b^2+14=0

We multiply all the terms by the denominator


54b+(-128b)+14*2592b^2=0

Wy multiply elements

36288b^2+54b+(-128b)=0

We get rid of parentheses

36288b^2+54b-128b=0

We add all the numbers together, and all the variables

36288b^2-74b=0

a = 36288; b = -74; c = 0;
Δ = b2-4ac
Δ = -742-4·36288·0
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-74}{2*36288}=\frac{0}{72576}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+74}{2*36288}=\frac{148}{72576}
=37/18144
$