36=5/4b+b

Solution for 36=5/4b+b equation:

36=5/4b+b

We move all terms to the left:

36-(5/4b+b)=0


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

b∈R


We add all the numbers together, and all the variables

-(+b+5/4b)+36=0

We get rid of parentheses

-b-5/4b+36=0

We multiply all the terms by the denominator


-b*4b+36*4b-5=0

Wy multiply elements

-4b^2+144b-5=0

a = -4; b = 144; c = -5;
Δ = b2-4ac
Δ = 1442-4·(-4)·(-5)
Δ = 20656
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:

$\sqrt{\Delta}=\sqrt{20656}=\sqrt{16*1291}=\sqrt{16}*\sqrt{1291}=4\sqrt{1291}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-4\sqrt{1291}}{2*-4}=\frac{-144-4\sqrt{1291}}{-8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+4\sqrt{1291}}{2*-4}=\frac{-144+4\sqrt{1291}}{-8}
$