(2/3)(a)+2/5=1

Solution for (2/3)(a)+2/5=1 equation:

(2/3)(a)+2/5=1

We move all terms to the left:

(2/3)(a)+2/5-(1)=0


Domain of the equation: 3)a!=0

a!=0/1

a!=0

a∈R


determiningTheFunctionDomain
(2/3)a-1+2/5=0

We add all the numbers together, and all the variables

(+2/3)a-1+2/5=0

We multiply parentheses

2a^2-1+2/5=0

We multiply all the terms by the denominator


2a^2*5+2-1*5=0

We add all the numbers together, and all the variables

2a^2*5-3=0

Wy multiply elements

10a^2-3=0

a = 10; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·10·(-3)
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*10}=\frac{0-2\sqrt{30}}{20}
=-\frac{2\sqrt{30}}{20}
=-\frac{\sqrt{30}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*10}=\frac{0+2\sqrt{30}}{20}
=\frac{2\sqrt{30}}{20}
=\frac{\sqrt{30}}{10}
$