3/5a+4=2a+11

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

3/5a+4=2a+11

We move all terms to the left:

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


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-2a*5a-11*5a+4*5a+3=0

Wy multiply elements

-10a^2-55a+20a+3=0

We add all the numbers together, and all the variables

-10a^2-35a+3=0

a = -10; b = -35; c = +3;
Δ = b2-4ac
Δ = -352-4·(-10)·3
Δ = 1345
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{-(-35)-\sqrt{1345}}{2*-10}=\frac{35-\sqrt{1345}}{-20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1345}}{2*-10}=\frac{35+\sqrt{1345}}{-20}
$