7/8b-32=0.75b+32

Solution for 7/8b-32=0.75b+32 equation:

7/8b-32=0.75b+32

We move all terms to the left:

7/8b-32-(0.75b+32)=0


Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R


We get rid of parentheses

7/8b-0.75b-32-32=0

We multiply all the terms by the denominator


-(0.75b)*8b-32*8b-32*8b+7=0

We add all the numbers together, and all the variables

-(+0.75b)*8b-32*8b-32*8b+7=0

We multiply parentheses

-0b^2-32*8b-32*8b+7=0

Wy multiply elements

-0b^2-256b-256b+7=0

We add all the numbers together, and all the variables

-1b^2-512b+7=0

a = -1; b = -512; c = +7;
Δ = b2-4ac
Δ = -5122-4·(-1)·7
Δ = 262172
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:

$\sqrt{\Delta}=\sqrt{262172}=\sqrt{4*65543}=\sqrt{4}*\sqrt{65543}=2\sqrt{65543}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-512)-2\sqrt{65543}}{2*-1}=\frac{512-2\sqrt{65543}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-512)+2\sqrt{65543}}{2*-1}=\frac{512+2\sqrt{65543}}{-2}
$