3/4b=10-b

Solution for 3/4b=10-b equation:

3/4b=10-b

We move all terms to the left:

3/4b-(10-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+10)=0

We get rid of parentheses

3/4b+1b-10=0

We multiply all the terms by the denominator


1b*4b-10*4b+3=0

Wy multiply elements

4b^2-40b+3=0

a = 4; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·4·3
Δ = 1552
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:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{97}}{2*4}=\frac{40-4\sqrt{97}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{97}}{2*4}=\frac{40+4\sqrt{97}}{8}
$