3/2b+5=20-b

Solution for 3/2b+5=20-b equation:

3/2b+5=20-b

We move all terms to the left:

3/2b+5-(20-b)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

3/2b-(-1b+20)+5=0

We get rid of parentheses

3/2b+1b-20+5=0

We multiply all the terms by the denominator


1b*2b-20*2b+5*2b+3=0

Wy multiply elements

2b^2-40b+10b+3=0

We add all the numbers together, and all the variables

2b^2-30b+3=0

a = 2; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·2·3
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{219}}{2*2}=\frac{30-2\sqrt{219}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*2}=\frac{30+2\sqrt{219}}{4}
$