3/5a+4=2a+11a

Solution for 3/5a+4=2a+11a equation:

3/5a+4=2a+11a

We move all terms to the left:

3/5a+4-(2a+11a)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

3/5a-(+13a)+4=0

We get rid of parentheses

3/5a-13a+4=0

We multiply all the terms by the denominator


-13a*5a+4*5a+3=0

Wy multiply elements

-65a^2+20a+3=0

a = -65; b = 20; c = +3;
Δ = b2-4ac
Δ = 202-4·(-65)·3
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{295}}{2*-65}=\frac{-20-2\sqrt{295}}{-130}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{295}}{2*-65}=\frac{-20+2\sqrt{295}}{-130}
$