(7/2a)=5a-3

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

(7/2a)=5a-3

We move all terms to the left:

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


Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

7/2a-5a+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

-10a^2+6a+7=0

a = -10; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·(-10)·7
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{79}}{2*-10}=\frac{-6-2\sqrt{79}}{-20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{79}}{2*-10}=\frac{-6+2\sqrt{79}}{-20}
$