m+3/2m=225

Solution for m+3/2m=225 equation:

m+3/2m=225

We move all terms to the left:

m+3/2m-(225)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We multiply all the terms by the denominator


m*2m-225*2m+3=0

Wy multiply elements

2m^2-450m+3=0

a = 2; b = -450; c = +3;
Δ = b2-4ac
Δ = -4502-4·2·3
Δ = 202476
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:

$\sqrt{\Delta}=\sqrt{202476}=\sqrt{4*50619}=\sqrt{4}*\sqrt{50619}=2\sqrt{50619}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-2\sqrt{50619}}{2*2}=\frac{450-2\sqrt{50619}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+2\sqrt{50619}}{2*2}=\frac{450+2\sqrt{50619}}{4}
$