-2/3(5b)=75+5/3b

Solution for -2/3(5b)=75+5/3b equation:

-2/3(5b)=75+5/3b

We move all terms to the left:

-2/3(5b)-(75+5/3b)=0


Domain of the equation: 35b!=0

b!=0/35

b!=0

b∈R



Domain of the equation: 3b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-2/35b-(5/3b+75)=0

We get rid of parentheses

-2/35b-5/3b-75=0

We calculate fractions


(-6b)/105b^2+(-175b)/105b^2-75=0

We multiply all the terms by the denominator


(-6b)+(-175b)-75*105b^2=0

Wy multiply elements

-7875b^2+(-6b)+(-175b)=0

We get rid of parentheses

-7875b^2-6b-175b=0

We add all the numbers together, and all the variables

-7875b^2-181b=0

a = -7875; b = -181; c = 0;
Δ = b2-4ac
Δ = -1812-4·(-7875)·0
Δ = 32761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32761}=181$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-181)-181}{2*-7875}=\frac{0}{-15750}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-181)+181}{2*-7875}=\frac{362}{-15750}
=-181/7875
$