8/7b-32=0.75b+32

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

8/7b-32=0.75b+32

We move all terms to the left:

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


Domain of the equation: 7b!=0

b!=0/7

b!=0

b∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

Wy multiply elements

-0b^2-224b-224b+8=0

We add all the numbers together, and all the variables

-1b^2-448b+8=0

a = -1; b = -448; c = +8;
Δ = b2-4ac
Δ = -4482-4·(-1)·8
Δ = 200736
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:

$\sqrt{\Delta}=\sqrt{200736}=\sqrt{144*1394}=\sqrt{144}*\sqrt{1394}=12\sqrt{1394}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-448)-12\sqrt{1394}}{2*-1}=\frac{448-12\sqrt{1394}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-448)+12\sqrt{1394}}{2*-1}=\frac{448+12\sqrt{1394}}{-2}
$