5/8b-6=1/2b+12

Solution for 5/8b-6=1/2b+12 equation:

5/8b-6=1/2b+12

We move all terms to the left:

5/8b-6-(1/2b+12)=0


Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R



Domain of the equation: 2b+12)!=0

b∈R


We get rid of parentheses

5/8b-1/2b-12-6=0

We calculate fractions


10b/16b^2+(-8b)/16b^2-12-6=0

We add all the numbers together, and all the variables

10b/16b^2+(-8b)/16b^2-18=0

We multiply all the terms by the denominator


10b+(-8b)-18*16b^2=0

Wy multiply elements

-288b^2+10b+(-8b)=0

We get rid of parentheses

-288b^2+10b-8b=0

We add all the numbers together, and all the variables

-288b^2+2b=0

a = -288; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-288)·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*-288}=\frac{-4}{-576}
=1/144
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-288}=\frac{0}{-576}
=0
$