1/4b-1/2b=-7/24

Solution for 1/4b-1/2b=-7/24 equation:

1/4b-1/2b=-7/24

We move all terms to the left:

1/4b-1/2b-(-7/24)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We get rid of parentheses

1/4b-1/2b+7/24=0

We calculate fractions


112b^2/384b^2+96b/384b^2+(-192b)/384b^2=0

We multiply all the terms by the denominator


112b^2+96b+(-192b)=0

We get rid of parentheses

112b^2+96b-192b=0

We add all the numbers together, and all the variables

112b^2-96b=0

a = 112; b = -96; c = 0;
Δ = b2-4ac
Δ = -962-4·112·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-96}{2*112}=\frac{0}{224}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+96}{2*112}=\frac{192}{224}
=6/7
$