3a-1=10/4a+1

Solution for 3a-1=10/4a+1 equation:

3a-1=10/4a+1

We move all terms to the left:

3a-1-(10/4a+1)=0


Domain of the equation: 4a+1)!=0

a∈R


We get rid of parentheses

3a-10/4a-1-1=0

We multiply all the terms by the denominator


3a*4a-1*4a-1*4a-10=0

Wy multiply elements

12a^2-4a-4a-10=0

We add all the numbers together, and all the variables

12a^2-8a-10=0

a = 12; b = -8; c = -10;
Δ = b2-4ac
Δ = -82-4·12·(-10)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{34}}{2*12}=\frac{8-4\sqrt{34}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{34}}{2*12}=\frac{8+4\sqrt{34}}{24}
$