T=2m-7/2m

Solution for T=2m-7/2m equation:

=2T-7/2T

We move all terms to the left:

-(2T-7/2T)=0


Domain of the equation: 2T)!=0

T!=0/1

T!=0

T∈R


We add all the numbers together, and all the variables

-(+2T-7/2T)=0

We get rid of parentheses

-2T+7/2T=0

We multiply all the terms by the denominator


-2T*2T+7=0

Wy multiply elements

-4T^2+7=0

a = -4; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-4)·7
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*-4}=\frac{0-4\sqrt{7}}{-8}
=-\frac{4\sqrt{7}}{-8}
=-\frac{\sqrt{7}}{-2}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*-4}=\frac{0+4\sqrt{7}}{-8}
=\frac{4\sqrt{7}}{-8}
=\frac{\sqrt{7}}{-2}
$