7/a-2=5a-3

Solution for 7/a-2=5a-3 equation:

7/a-2=5a-3

We move all terms to the left:

7/a-2-(5a-3)=0


Domain of the equation: a!=0

a∈R


We get rid of parentheses

7/a-5a+3-2=0

We multiply all the terms by the denominator


-5a*a+3*a-2*a+7=0

We add all the numbers together, and all the variables

a-5a*a+7=0

Wy multiply elements

-5a^2+a+7=0

a = -5; b = 1; c = +7;
Δ = b2-4ac
Δ = 12-4·(-5)·7
Δ = 141
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{-(1)-\sqrt{141}}{2*-5}=\frac{-1-\sqrt{141}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{141}}{2*-5}=\frac{-1+\sqrt{141}}{-10}
$