-1/2b-8=3/4b+52

Solution for -1/2b-8=3/4b+52 equation:

-1/2b-8=3/4b+52

We move all terms to the left:

-1/2b-8-(3/4b+52)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 4b+52)!=0

b∈R


We get rid of parentheses

-1/2b-3/4b-52-8=0

We calculate fractions


(-4b)/8b^2+(-6b)/8b^2-52-8=0

We add all the numbers together, and all the variables

(-4b)/8b^2+(-6b)/8b^2-60=0

We multiply all the terms by the denominator


(-4b)+(-6b)-60*8b^2=0

Wy multiply elements

-480b^2+(-4b)+(-6b)=0

We get rid of parentheses

-480b^2-4b-6b=0

We add all the numbers together, and all the variables

-480b^2-10b=0

a = -480; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-480)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-480}=\frac{0}{-960}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-480}=\frac{20}{-960}
=-1/48
$