m+7=3/2m

Solution for m+7=3/2m equation:

m+7=3/2m

We move all terms to the left:

m+7-(3/2m)=0


Domain of the equation: 2m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

m-(+3/2m)+7=0

We get rid of parentheses

m-3/2m+7=0

We multiply all the terms by the denominator


m*2m+7*2m-3=0

Wy multiply elements

2m^2+14m-3=0

a = 2; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·2·(-3)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{55}}{2*2}=\frac{-14-2\sqrt{55}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{55}}{2*2}=\frac{-14+2\sqrt{55}}{4}
$