x(1+0.12*65/365)=1225.64

Solution for x(1+0.12*65/365)=1225.64 equation:

x(1+0.12*65/365)=1225.64

We move all terms to the left:

x(1+0.12*65/365)-(1225.64)=0

We add all the numbers together, and all the variables

x(0.12*65/365+1)-(1225.64)=0

We add all the numbers together, and all the variables

x(0.12*65/365+1)-1225.64=0

We multiply parentheses

7.8x^2+x-1225.64=0

a = 7.8; b = 1; c = -1225.64;
Δ = b2-4ac
Δ = 12-4·7.8·(-1225.64)
Δ = 38240.968
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{38240.968}}{2*7.8}=\frac{-1-\sqrt{38240.968}}{15.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{38240.968}}{2*7.8}=\frac{-1+\sqrt{38240.968}}{15.6}
$