4/5b+7=7/8b+19

Solution for 4/5b+7=7/8b+19 equation:

4/5b+7=7/8b+19

We move all terms to the left:

4/5b+7-(7/8b+19)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 8b+19)!=0

b∈R


We get rid of parentheses

4/5b-7/8b-19+7=0

We calculate fractions


32b/40b^2+(-35b)/40b^2-19+7=0

We add all the numbers together, and all the variables

32b/40b^2+(-35b)/40b^2-12=0

We multiply all the terms by the denominator


32b+(-35b)-12*40b^2=0

Wy multiply elements

-480b^2+32b+(-35b)=0

We get rid of parentheses

-480b^2+32b-35b=0

We add all the numbers together, and all the variables

-480b^2-3b=0

a = -480; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-480)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-480}=\frac{0}{-960}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-480}=\frac{6}{-960}
=-1/160
$