5m+2m=1/2m-20

Solution for 5m+2m=1/2m-20 equation:

5m+2m=1/2m-20

We move all terms to the left:

5m+2m-(1/2m-20)=0


Domain of the equation: 2m-20)!=0

m∈R


We add all the numbers together, and all the variables

7m-(1/2m-20)=0

We get rid of parentheses

7m-1/2m+20=0

We multiply all the terms by the denominator


7m*2m+20*2m-1=0

Wy multiply elements

14m^2+40m-1=0

a = 14; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·14·(-1)
Δ = 1656
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:

$\sqrt{\Delta}=\sqrt{1656}=\sqrt{36*46}=\sqrt{36}*\sqrt{46}=6\sqrt{46}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-6\sqrt{46}}{2*14}=\frac{-40-6\sqrt{46}}{28}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+6\sqrt{46}}{2*14}=\frac{-40+6\sqrt{46}}{28}
$