11/4b+8=1/2b-7

Solution for 11/4b+8=1/2b-7 equation:

11/4b+8=1/2b-7

We move all terms to the left:

11/4b+8-(1/2b-7)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 2b-7)!=0

b∈R


We get rid of parentheses

11/4b-1/2b+7+8=0

We calculate fractions


22b/8b^2+(-4b)/8b^2+7+8=0

We add all the numbers together, and all the variables

22b/8b^2+(-4b)/8b^2+15=0

We multiply all the terms by the denominator


22b+(-4b)+15*8b^2=0

Wy multiply elements

120b^2+22b+(-4b)=0

We get rid of parentheses

120b^2+22b-4b=0

We add all the numbers together, and all the variables

120b^2+18b=0

a = 120; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·120·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*120}=\frac{-36}{240}
=-3/20
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*120}=\frac{0}{240}
=0
$