5/4b+7=0.875b+19

Solution for 5/4b+7=0.875b+19 equation:

5/4b+7=0.875b+19

We move all terms to the left:

5/4b+7-(0.875b+19)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We get rid of parentheses

5/4b-0.875b-19+7=0

We multiply all the terms by the denominator


-(0.875b)*4b-19*4b+7*4b+5=0

We add all the numbers together, and all the variables

-(+0.875b)*4b-19*4b+7*4b+5=0

We multiply parentheses

-0b^2-19*4b+7*4b+5=0

Wy multiply elements

-0b^2-76b+28b+5=0

We add all the numbers together, and all the variables

-1b^2-48b+5=0

a = -1; b = -48; c = +5;
Δ = b2-4ac
Δ = -482-4·(-1)·5
Δ = 2324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2324}=\sqrt{4*581}=\sqrt{4}*\sqrt{581}=2\sqrt{581}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{581}}{2*-1}=\frac{48-2\sqrt{581}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{581}}{2*-1}=\frac{48+2\sqrt{581}}{-2}
$