5m(2m-9)=3m-2

Solution for 5m(2m-9)=3m-2 equation:

5m(2m-9)=3m-2

We move all terms to the left:

5m(2m-9)-(3m-2)=0

We multiply parentheses

10m^2-45m-(3m-2)=0

We get rid of parentheses

10m^2-45m-3m+2=0

We add all the numbers together, and all the variables

10m^2-48m+2=0

a = 10; b = -48; c = +2;
Δ = b2-4ac
Δ = -482-4·10·2
Δ = 2224
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:

$\sqrt{\Delta}=\sqrt{2224}=\sqrt{16*139}=\sqrt{16}*\sqrt{139}=4\sqrt{139}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{139}}{2*10}=\frac{48-4\sqrt{139}}{20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{139}}{2*10}=\frac{48+4\sqrt{139}}{20}
$