(2/3)b=10.b

Solution for (2/3)b=10.b equation:

(2/3)b=10.b

We move all terms to the left:

(2/3)b-(10.b)=0


Domain of the equation: 3)b!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

2b^2-(+10.b)=0

We get rid of parentheses

2b^2-10.b=0

We add all the numbers together, and all the variables

2b^2-10b=0

a = 2; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·2·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*2}=\frac{0}{4}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*2}=\frac{20}{4}
=5
$