1-3m+9m(m-1)/2=559

Solution for 1-3m+9m(m-1)/2=559 equation:

1-3m+9m(m-1)/2=559

We move all terms to the left:

1-3m+9m(m-1)/2-(559)=0

We add all the numbers together, and all the variables

-3m+9m(m-1)/2-558=0

We multiply all the terms by the denominator


-3m*2+9m(m-1)-558*2=0

We add all the numbers together, and all the variables

-3m*2+9m(m-1)-1116=0

We multiply parentheses

9m^2-3m*2-9m-1116=0

Wy multiply elements

9m^2-6m-9m-1116=0

We add all the numbers together, and all the variables

9m^2-15m-1116=0

a = 9; b = -15; c = -1116;
Δ = b2-4ac
Δ = -152-4·9·(-1116)
Δ = 40401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40401}=201$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-201}{2*9}=\frac{-186}{18}
=-10+1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+201}{2*9}=\frac{216}{18}
=12
$