2.6a-1.3=6a-18-4/5a

Solution for 2.6a-1.3=6a-18-4/5a equation:

2.6a-1.3=6a-18-4/5a

We move all terms to the left:

2.6a-1.3-(6a-18-4/5a)=0


Domain of the equation: 5a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

2.6a-(6a-4/5a-18)-1.3=0

We get rid of parentheses

2.6a-6a+4/5a+18-1.3=0

We multiply all the terms by the denominator


(2.6a)*5a-6a*5a+18*5a-(1.3)*5a+4=0

We add all the numbers together, and all the variables

(+2.6a)*5a-6a*5a+18*5a-(1.3)*5a+4=0

We multiply parentheses

10a^2-6a*5a+18*5a-6.5a+4=0

Wy multiply elements

10a^2-30a^2+90a-6.5a+4=0

We add all the numbers together, and all the variables

-20a^2+83.5a+4=0

a = -20; b = 83.5; c = +4;
Δ = b2-4ac
Δ = 83.52-4·(-20)·4
Δ = 7292.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(83.5)-\sqrt{7292.25}}{2*-20}=\frac{-83.5-\sqrt{7292.25}}{-40}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(83.5)+\sqrt{7292.25}}{2*-20}=\frac{-83.5+\sqrt{7292.25}}{-40}
$