-1/5b+8=-4b-11

Solution for -1/5b+8=-4b-11 equation:

-1/5b+8=-4b-11

We move all terms to the left:

-1/5b+8-(-4b-11)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We get rid of parentheses

-1/5b+4b+11+8=0

We multiply all the terms by the denominator


4b*5b+11*5b+8*5b-1=0

Wy multiply elements

20b^2+55b+40b-1=0

We add all the numbers together, and all the variables

20b^2+95b-1=0

a = 20; b = 95; c = -1;
Δ = b2-4ac
Δ = 952-4·20·(-1)
Δ = 9105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(95)-\sqrt{9105}}{2*20}=\frac{-95-\sqrt{9105}}{40}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(95)+\sqrt{9105}}{2*20}=\frac{-95+\sqrt{9105}}{40}
$