2a+3/3a+7=35

Solution for 2a+3/3a+7=35 equation:

2a+3/3a+7=35

We move all terms to the left:

2a+3/3a+7-(35)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

2a+3/3a-28=0

We multiply all the terms by the denominator


2a*3a-28*3a+3=0

Wy multiply elements

6a^2-84a+3=0

a = 6; b = -84; c = +3;
Δ = b2-4ac
Δ = -842-4·6·3
Δ = 6984
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:

$\sqrt{\Delta}=\sqrt{6984}=\sqrt{36*194}=\sqrt{36}*\sqrt{194}=6\sqrt{194}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-6\sqrt{194}}{2*6}=\frac{84-6\sqrt{194}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+6\sqrt{194}}{2*6}=\frac{84+6\sqrt{194}}{12}
$