1/212m-10=4m+14-2m

Solution for 1/212m-10=4m+14-2m equation:

1/212m-10=4m+14-2m

We move all terms to the left:

1/212m-10-(4m+14-2m)=0


Domain of the equation: 212m!=0

m!=0/212

m!=0

m∈R


We add all the numbers together, and all the variables

1/212m-(2m+14)-10=0

We get rid of parentheses

1/212m-2m-14-10=0

We multiply all the terms by the denominator


-2m*212m-14*212m-10*212m+1=0

Wy multiply elements

-424m^2-2968m-2120m+1=0

We add all the numbers together, and all the variables

-424m^2-5088m+1=0

a = -424; b = -5088; c = +1;
Δ = b2-4ac
Δ = -50882-4·(-424)·1
Δ = 25889440
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{25889440}=\sqrt{16*1618090}=\sqrt{16}*\sqrt{1618090}=4\sqrt{1618090}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5088)-4\sqrt{1618090}}{2*-424}=\frac{5088-4\sqrt{1618090}}{-848}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5088)+4\sqrt{1618090}}{2*-424}=\frac{5088+4\sqrt{1618090}}{-848}
$