2-5m=2m^2+3m

Solution for 2-5m=2m^2+3m equation:

2-5m=2m^2+3m

We move all terms to the left:

2-5m-(2m^2+3m)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·(-2)·2
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{5}}{2*-2}=\frac{8-4\sqrt{5}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{5}}{2*-2}=\frac{8+4\sqrt{5}}{-4}
$