x^2-11.25x=1/45

Solution for x^2-11.25x=1/45 equation:

x^2-11.25x=1/45

We move all terms to the left:

x^2-11.25x-(1/45)=0

We add all the numbers together, and all the variables

x^2-11.25x-(+1/45)=0

We get rid of parentheses

x^2-11.25x-1/45=0

We multiply all the terms by the denominator


x^2*45-(11.25x)*45-1=0

We add all the numbers together, and all the variables

x^2*45-(+11.25x)*45-1=0

We multiply parentheses

x^2*45-495x-1=0

Wy multiply elements

45x^2-495x-1=0

a = 45; b = -495; c = -1;
Δ = b2-4ac
Δ = -4952-4·45·(-1)
Δ = 245205
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{245205}=\sqrt{9*27245}=\sqrt{9}*\sqrt{27245}=3\sqrt{27245}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-495)-3\sqrt{27245}}{2*45}=\frac{495-3\sqrt{27245}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-495)+3\sqrt{27245}}{2*45}=\frac{495+3\sqrt{27245}}{90}
$