10m2-3m=2(2-3m)

Solution for 10m2-3m=2(2-3m) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(2(-3m+2)), so:

2(-3m+2)

We multiply parentheses

-6m+4

Back to the equation:

-(-6m+4)


We get rid of parentheses

10m^2-3m+6m-4=0

We add all the numbers together, and all the variables

10m^2+3m-4=0

a = 10; b = 3; c = -4;
Δ = b2-4ac
Δ = 32-4·10·(-4)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-13}{2*10}=\frac{-16}{20}
=-4/5
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+13}{2*10}=\frac{10}{20}
=1/2
$