5a-7/2a=31-1

Solution for 5a-7/2a=31-1 equation:

5a-7/2a=31-1

We move all terms to the left:

5a-7/2a-(31-1)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

5a-7/2a-30=0

We multiply all the terms by the denominator


5a*2a-30*2a-7=0

Wy multiply elements

10a^2-60a-7=0

a = 10; b = -60; c = -7;
Δ = b2-4ac
Δ = -602-4·10·(-7)
Δ = 3880
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:

$\sqrt{\Delta}=\sqrt{3880}=\sqrt{4*970}=\sqrt{4}*\sqrt{970}=2\sqrt{970}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{970}}{2*10}=\frac{60-2\sqrt{970}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{970}}{2*10}=\frac{60+2\sqrt{970}}{20}
$