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

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

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

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

m+3/2m-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

2m^2-10m+3=0

a = 2; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·2·3
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{19}}{2*2}=\frac{10-2\sqrt{19}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{19}}{2*2}=\frac{10+2\sqrt{19}}{4}
$