2/5b+2-3/10b=5

Solution for 2/5b+2-3/10b=5 equation:

2/5b+2-3/10b=5

We move all terms to the left:

2/5b+2-3/10b-(5)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 10b!=0

b!=0/10

b!=0

b∈R


We add all the numbers together, and all the variables

2/5b-3/10b-3=0

We calculate fractions


20b/50b^2+(-15b)/50b^2-3=0

We multiply all the terms by the denominator


20b+(-15b)-3*50b^2=0

Wy multiply elements

-150b^2+20b+(-15b)=0

We get rid of parentheses

-150b^2+20b-15b=0

We add all the numbers together, and all the variables

-150b^2+5b=0

a = -150; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-150)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-150}=\frac{-10}{-300}
=1/30
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-150}=\frac{0}{-300}
=0
$