7/2a2-5=37

Solution for 7/2a2-5=37 equation:

7/2a^2-5=37

We move all terms to the left:

7/2a^2-5-(37)=0


Domain of the equation: 2a^2!=0

a^2!=0/2

a^2!=√0

a!=0

a∈R


We add all the numbers together, and all the variables

7/2a^2-42=0

We multiply all the terms by the denominator


-42*2a^2+7=0

Wy multiply elements

-84a^2+7=0

a = -84; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-84)·7
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{3}}{2*-84}=\frac{0-28\sqrt{3}}{-168}
=-\frac{28\sqrt{3}}{-168}
=-\frac{\sqrt{3}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{3}}{2*-84}=\frac{0+28\sqrt{3}}{-168}
=\frac{28\sqrt{3}}{-168}
=\frac{\sqrt{3}}{-6}
$