3/5a+1/2a=11

Solution for 3/5a+1/2a=11 equation:

3/5a+1/2a=11

We move all terms to the left:

3/5a+1/2a-(11)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We calculate fractions


6a/10a^2+5a/10a^2-11=0

We multiply all the terms by the denominator


6a+5a-11*10a^2=0

We add all the numbers together, and all the variables

11a-11*10a^2=0

Wy multiply elements

-110a^2+11a=0

a = -110; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-110)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-110}=\frac{-22}{-220}
=1/10
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-110}=\frac{0}{-220}
=0
$