-1/2b-8=-3/4b+7

Solution for -1/2b-8=-3/4b+7 equation:

-1/2b-8=-3/4b+7

We move all terms to the left:

-1/2b-8-(-3/4b+7)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 4b+7)!=0

b∈R


We get rid of parentheses

-1/2b+3/4b-7-8=0

We calculate fractions


(-4b)/8b^2+6b/8b^2-7-8=0

We add all the numbers together, and all the variables

(-4b)/8b^2+6b/8b^2-15=0

We multiply all the terms by the denominator


(-4b)+6b-15*8b^2=0

We add all the numbers together, and all the variables

6b+(-4b)-15*8b^2=0

Wy multiply elements

-120b^2+6b+(-4b)=0

We get rid of parentheses

-120b^2+6b-4b=0

We add all the numbers together, and all the variables

-120b^2+2b=0

a = -120; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-120)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-120}=\frac{-4}{-240}
=1/60
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-120}=\frac{0}{-240}
=0
$