3/4b+5=20-b

Solution for 3/4b+5=20-b equation:

3/4b+5=20-b

We move all terms to the left:

3/4b+5-(20-b)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We add all the numbers together, and all the variables

3/4b-(-1b+20)+5=0

We get rid of parentheses

3/4b+1b-20+5=0

We multiply all the terms by the denominator


1b*4b-20*4b+5*4b+3=0

Wy multiply elements

4b^2-80b+20b+3=0

We add all the numbers together, and all the variables

4b^2-60b+3=0

a = 4; b = -60; c = +3;
Δ = b2-4ac
Δ = -602-4·4·3
Δ = 3552
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:

$\sqrt{\Delta}=\sqrt{3552}=\sqrt{16*222}=\sqrt{16}*\sqrt{222}=4\sqrt{222}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{222}}{2*4}=\frac{60-4\sqrt{222}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{222}}{2*4}=\frac{60+4\sqrt{222}}{8}
$