3/4m+2=2m+5

Solution for 3/4m+2=2m+5 equation:

3/4m+2=2m+5

We move all terms to the left:

3/4m+2-(2m+5)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We get rid of parentheses

3/4m-2m-5+2=0

We multiply all the terms by the denominator


-2m*4m-5*4m+2*4m+3=0

Wy multiply elements

-8m^2-20m+8m+3=0

We add all the numbers together, and all the variables

-8m^2-12m+3=0

a = -8; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·(-8)·3
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*-8}=\frac{12-4\sqrt{15}}{-16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*-8}=\frac{12+4\sqrt{15}}{-16}
$