5a-7/3a+1=45

Solution for 5a-7/3a+1=45 equation:

5a-7/3a+1=45

We move all terms to the left:

5a-7/3a+1-(45)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

5a-7/3a-44=0

We multiply all the terms by the denominator


5a*3a-44*3a-7=0

Wy multiply elements

15a^2-132a-7=0

a = 15; b = -132; c = -7;
Δ = b2-4ac
Δ = -1322-4·15·(-7)
Δ = 17844
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:

$\sqrt{\Delta}=\sqrt{17844}=\sqrt{4*4461}=\sqrt{4}*\sqrt{4461}=2\sqrt{4461}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-2\sqrt{4461}}{2*15}=\frac{132-2\sqrt{4461}}{30}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+2\sqrt{4461}}{2*15}=\frac{132+2\sqrt{4461}}{30}
$