7a+3=4a+18/a

Solution for 7a+3=4a+18/a equation:

7a+3=4a+18/a

We move all terms to the left:

7a+3-(4a+18/a)=0


Domain of the equation: a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

7a-(+4a+18/a)+3=0

We get rid of parentheses

7a-4a-18/a+3=0

We multiply all the terms by the denominator


7a*a-4a*a+3*a-18=0

We add all the numbers together, and all the variables

3a+7a*a-4a*a-18=0

Wy multiply elements

7a^2-4a^2+3a-18=0

We add all the numbers together, and all the variables

3a^2+3a-18=0

a = 3; b = 3; c = -18;
Δ = b2-4ac
Δ = 32-4·3·(-18)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*3}=\frac{-18}{6}
=-3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*3}=\frac{12}{6}
=2
$