5/2*b-5=1/2*b+1

Solution for 5/2*b-5=1/2*b+1 equation:

5/2*b-5=1/2*b+1

We move all terms to the left:

5/2*b-5-(1/2*b+1)=0


Domain of the equation: 2*b!=0

b!=0/1

b!=0

b∈R



Domain of the equation: 2*b+1)!=0

b∈R


We get rid of parentheses

5/2*b-1/2*b-1-5=0

We multiply all the terms by the denominator


-1*2*b-5*2*b+5-1=0

We add all the numbers together, and all the variables

-1*2*b-5*2*b+4=0

Wy multiply elements

-2b*b-10b*b+4=0

Wy multiply elements

-2b^2-10b^2+4=0

We add all the numbers together, and all the variables

-12b^2+4=0

a = -12; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-12)·4
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-12}=\frac{0-8\sqrt{3}}{-24}
=-\frac{8\sqrt{3}}{-24}
=-\frac{\sqrt{3}}{-3}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-12}=\frac{0+8\sqrt{3}}{-24}
=\frac{8\sqrt{3}}{-24}
=\frac{\sqrt{3}}{-3}
$